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252 relations: Abstract algebra, Alexander Givental, Alexander polynomial, Algebraic topology, Algebraic variety, Analysis Situs (paper), Analytic continuation, André Joyal, André Lichnerowicz, Atlas (topology), Axiom of countability, Élie Cartan, Čech cohomology, Bartel Leendert van der Waerden, Behrend function, Beno Eckmann, Bernhard Riemann, Betti number, Braided monoidal category, Calculus, Cambridge University Press, Carl Friedrich Gauss, Categorical quantum mechanics, Category (mathematics), Category theory, Chain complex, Chern class, Chern–Simons theory, Chromatic homotopy theory, Ciprian Manolescu, Classical group, Classifying space, Cobordism, Cobordism hypothesis, Coherent sheaf, Cohomology ring, Combinatorial topology, Complex manifold, Complex projective plane, Configuration space (physics), Conformal field theory, Connected sum, Cotangent bundle, Covering space, Critical point (mathematics), Cup product, CW complex, David Hilbert, De Rham cohomology, Degree of a continuous mapping, ..., Dehn–Sommerville equations, Dennis Barden, Dennis Sullivan, Differentiable manifold, Differentiable stack, Differential form, Differential geometry, Differential topology, Donaldson theory, Donaldson–Thomas theory, Eduard Čech, Edward Witten, Egbert van Kampen, Eilenberg–Steenrod axioms, Emmy Noether, Enumerative geometry, Erlangen program, Ernst Steinitz, Euler characteristic, Exotic sphere, Exterior algebra, Factorization homology, Felix Klein, Finite type invariant, Floer homology, French mathematical seminars, Frobenius algebra, Fukaya category, Functor, Fundamental class, Fundamental group, Gauss–Bonnet theorem, Geometric topology, Georges de Rham, German Mathematical Society, Glossary of algebraic topology, Glossary of category theory, Graeme Segal, Grassmannian, Group action, H-cobordism, Habilitation, Hamiltonian mechanics, Hassler Whitney, Hauptvermutung, Hausdorff space, Heinrich Franz Friedrich Tietze, Heinz Hopf, Hellmuth Kneser, Helmut Hofer, Henri Cartan, Henri Poincaré, Henry Roy Brahana, Hermann Grassmann, Hermann Künneth, Hermann Weyl, Hilbert's axioms, Hilbert's fifteenth problem, Hilbert's fifth problem, Hilbert's third problem, History of manifolds and varieties, Homogeneous space, Homological mirror symmetry, Homology manifold, Homotopy, Homotopy groups of spheres, Hopf algebra, Hyperbolic geometry, Igor Frenkel, Implicit function theorem, Intersection number, Intersection theory, Invariance of domain, J. H. C. Whitehead, J. Peter May, Jacob Lurie, James Harris Simons, János Bolyai, Jean Leray, Jean-Victor Poncelet, Joachim Lambek, John C. Baez, John Horton Conway, John Milnor, Jones polynomial, Joseph Bernstein, Joseph Diez Gergonne, Journal of the American Mathematical Society, Künneth theorem, Kenji Fukaya, Khovanov homology, Klein's encyclopedia, Knot invariant, Knot polynomial, Kontsevich invariant, Kuranishi structure, L. E. J. Brouwer, Langlands program, Leonhard Euler, Leopold Vietoris, Lie group, List of loop quantum gravity researchers, Local system, Low-dimensional topology, Manifold, Marston Morse, Mathematical analysis, Max Dehn, Maxim Kontsevich, Michael J. Hopkins, Michel Kervaire, Michio Jimbo, Mikhail Khovanov, Module (mathematics), Monoidal category, Morse theory, Natural transformation, Nicolai Reshetikhin, Non-Euclidean geometry, Norman Steenrod, Oleg Viro, Orbifold, Orientability, Oswald Veblen, Otto Schreier, Paul Koebe, Peter J. Freyd, Peter Ozsváth, Piecewise linear manifold, Pierre Ossian Bonnet, Poincaré conjecture, Poincaré duality, Poincaré–Hopf theorem, Poisson manifold, Poul Heegaard, Projective geometry, Pseudogroup, Pseudomanifold, Quantum field theory, Quantum group, Quantum invariant, Quantum topology, R-matrix, Ramification (mathematics), Real projective plane, René Thom, Ribbon category, Richard Thomas (mathematician), Riemann sphere, Riemann surface, Riemannian manifold, Ronald Brown (mathematician), Ross Street, Ruth Lawrence, Samuel Eilenberg, Saunders Mac Lane, Schubert calculus, Second-countable space, Sheaf (mathematics), Sheaf cohomology, Shiing-Shen Chern, Simon Donaldson, Simplicial homology, Simplicial polytope, Simplicial set, Simply connected space, Singular homology, Skein relation, Smoothness, Snake lemma, Solomon Lefschetz, Sophus Lie, Spectral sequence, Spherical category, Steenrod problem, Stephen Smale, String diagram, String topology, Symmetric space, Tangle (mathematics), Temperley–Lieb algebra, Thom space, Tibor Radó, Topological group, Topological manifold, Topological modular forms, Topological quantum field theory, Topological space, Topological string theory, Triangulation (geometry), Ulisse Dini, Uniformization theorem, Vaughan Jones, Vladimir Drinfeld, Vladimir Turaev, Whitney embedding theorem, Wigner–Weyl transform, Witold Hurewicz, Yakov Eliashberg, Zero of a function, Zoltán Szabó (mathematician), 5-manifold. Expand index (202 more) »
Abstract algebra
In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.
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Alexander Givental
Alexander Givental (Александр Борисович Гивенталь) is a Russian American mathematician working in the area of symplectic topology, singularity theory and their relations to topological string theories.
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Alexander polynomial
In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type.
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Algebraic topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces.
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Algebraic variety
Algebraic varieties are the central objects of study in algebraic geometry.
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Analysis Situs (paper)
"Analysis Situs" is a seminal mathematics paper that Henri Poincaré published in 1895.
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Analytic continuation
In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of a given analytic function.
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André Joyal
André Joyal (born 1943) is a professor of mathematics at the Université du Québec à Montréal who works on category theory.
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André Lichnerowicz
André Lichnerowicz (January 21, 1915 – December 11, 1998) was a noted French differential geometer and mathematical physicist of Polish descent.
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Atlas (topology)
In mathematics, particularly topology, one describes a manifold using an atlas.
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Axiom of countability
In mathematics, an axiom of countability is a property of certain mathematical objects (usually in a category) that asserts the existence of a countable set with certain properties.
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Élie Cartan
Élie Joseph Cartan, ForMemRS (9 April 1869 – 6 May 1951) was an influential French mathematician who did fundamental work in the theory of Lie groups and their geometric applications.
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Čech cohomology
In mathematics, specifically algebraic topology, Čech cohomology is a cohomology theory based on the intersection properties of open covers of a topological space.
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Bartel Leendert van der Waerden
Bartel Leendert van der Waerden (February 2, 1903 – January 12, 1996) was a Dutch mathematician and historian of mathematics.
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Behrend function
In algebraic geometry, the Behrend function of a scheme X, introduced by Kai Behrend, is a constructible function such that if X is a quasi-projective proper moduli scheme carrying a symmetric obstruction theory, then the weighted Euler characteristic is the degree of the virtual fundamental class of X, which is an element of the zeroth Chow group of X. Modulo some solvable technical difficulties (e.g., what is the Chow group of a stack?), the definition extends to moduli stacks such as the moduli stack of stable sheaves (the Donaldson–Thomas theory) or that of stable maps (the Gromov–Witten theory).
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Beno Eckmann
Beno Eckmann (31 March 1917 – 25 November 2008 in Zurich) was a Swiss mathematician who was a student of Heinz Hopf.
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Bernhard Riemann
Georg Friedrich Bernhard Riemann (17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry.
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Betti number
In algebraic topology, the Betti numbers are used to distinguish topological spaces based on the connectivity of n-dimensional simplicial complexes.
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Braided monoidal category
In mathematics, a commutativity constraint \gamma on a monoidal category \mathcal is a choice of isomorphism \gamma_: A\otimes B \rightarrow B\otimes A for each pair of objects A and B which form a "natural family." In particular, to have a commutativity constraint, one must have A \otimes B \cong B \otimes A for all pairs of objects A,B \in \mathcal.
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Calculus
Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Carl Friedrich Gauss
Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields, including algebra, analysis, astronomy, differential geometry, electrostatics, geodesy, geophysics, magnetic fields, matrix theory, mechanics, number theory, optics and statistics.
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Categorical quantum mechanics
Categorical quantum mechanics is the study of quantum foundations and quantum information using paradigms from mathematics and computer science, notably monoidal category theory.
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Category (mathematics)
In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is an algebraic structure similar to a group but without requiring inverse or closure properties.
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Category theory
Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).
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Chain complex
In mathematics, a chain complex is an algebraic structure that consists of a sequence of abelian groups (or modules) and a sequence of homomorphisms between consecutive groups such that the image of each homomorphism is included in the kernel of the next.
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Chern class
In mathematics, in particular in algebraic topology, differential geometry and algebraic geometry, the Chern classes are characteristic classes associated with complex vector bundles.
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Chern–Simons theory
The Chern–Simons theory, named after Shiing-Shen Chern and James Harris Simons, is a 3-dimensional topological quantum field theory of Schwarz type, developed by Edward Witten.
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Chromatic homotopy theory
In mathematics, chromatic homotopy theory is a subfield of stable homotopy theory that studies complex-oriented cohomology theories from the "chromatic" point of view, which is based on Quillen's work relating cohomology theories to formal groups.
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Ciprian Manolescu
Ciprian Manolescu (born December 24, 1978) is a Romanian-American mathematician, working in gauge theory, symplectic geometry, and low-dimensional topology.
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Classical group
In mathematics, the classical groups are defined as the special linear groups over the reals, the complex numbers and the quaternions together with special automorphism groups of symmetric or skew-symmetric bilinear forms and Hermitian or skew-Hermitian sesquilinear forms defined on real, complex and quaternionic finite-dimensional vector spaces.
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Classifying space
In mathematics, specifically in homotopy theory, a classifying space BG of a topological group G is the quotient of a weakly contractible space EG (i.e. a topological space all of whose homotopy groups are trivial) by a proper free action of G. It has the property that any G principal bundle over a paracompact manifold is isomorphic to a pullback of the principal bundle EG → BG.
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Cobordism
In mathematics, cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary (French bord, giving cobordism) of a manifold.
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Cobordism hypothesis
In mathematics, the cobordism hypothesis, due to John C. Baez and James Dolan, concerns the classification of extended topological quantum field theories (TQFTs).
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Coherent sheaf
In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space.
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Cohomology ring
In mathematics, specifically algebraic topology, the cohomology ring of a topological space X is a ring formed from the cohomology groups of X together with the cup product serving as the ring multiplication.
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Combinatorial topology
In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces (for example the Betti numbers) were regarded as derived from combinatorial decompositions of spaces, such as decomposition into simplicial complexes.
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Complex manifold
In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk in Cn, such that the transition maps are holomorphic.
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Complex projective plane
In mathematics, the complex projective plane, usually denoted P2(C), is the two-dimensional complex projective space.
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Configuration space (physics)
In classical mechanics, the parameters that define the configuration of a system are called generalized coordinates, and the vector space defined by these coordinates is called the configuration space of the physical system.
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Conformal field theory
A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations.
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Connected sum
In mathematics, specifically in topology, the operation of connected sum is a geometric modification on manifolds.
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Cotangent bundle
In mathematics, especially differential geometry, the cotangent bundle of a smooth manifold is the vector bundle of all the cotangent spaces at every point in the manifold.
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Covering space
In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below.
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Critical point (mathematics)
In mathematics, a critical point or stationary point of a differentiable function of a real or complex variable is any value in its domain where its derivative is 0.
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Cup product
In mathematics, specifically in algebraic topology, the cup product is a method of adjoining two cocycles of degree p and q to form a composite cocycle of degree p + q. This defines an associative (and distributive) graded commutative product operation in cohomology, turning the cohomology of a space X into a graded ring, H∗(X), called the cohomology ring.
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CW complex
In topology, a CW complex is a type of topological space introduced by J. H. C. Whitehead to meet the needs of homotopy theory.
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David Hilbert
David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician.
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De Rham cohomology
In mathematics, de Rham cohomology (after Georges de Rham) is a tool belonging both to algebraic topology and to differential topology, capable of expressing basic topological information about smooth manifolds in a form particularly adapted to computation and the concrete representation of cohomology classes.
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Degree of a continuous mapping
In topology, the degree of a continuous mapping between two compact oriented manifolds of the same dimension is a number that represents the number of times that the domain manifold wraps around the range manifold under the mapping.
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Dehn–Sommerville equations
In mathematics, the Dehn–Sommerville equations are a complete set of linear relations between the numbers of faces of different dimension of a simplicial polytope.
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Dennis Barden
Dennis Barden is a mathematician at the University of Cambridge working in the fields of geometry and topology.
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Dennis Sullivan
Dennis Parnell Sullivan (born February 12, 1941) is an American mathematician.
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Differentiable manifold
In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.
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Differentiable stack
In differential geometry, a differentiable stack is a stack over the category of differentiable manifolds (with the usual open covering topology) which admits an atlas.
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Differential form
In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates.
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Differential geometry
Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.
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Differential topology
In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds.
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Donaldson theory
Donaldson theory is the study of the topology of smooth 4-manifolds using moduli spaces of anti-self-dual instantons.
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Donaldson–Thomas theory
In mathematics, specifically algebraic geometry, Donaldson–Thomas theory is the theory of Donaldson–Thomas invariants.
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Eduard Čech
Eduard Čech (29 June 1893 – 15 March 1960) was a Czech mathematician born in Stračov (then Bohemia, Austria-Hungary, now Czech Republic).
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Edward Witten
Edward Witten (born August 26, 1951) is an American theoretical physicist and professor of mathematical physics at the Institute for Advanced Study in Princeton, New Jersey.
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Egbert van Kampen
Egbert Rudolf van Kampen (28 May 1908, Berchem, Belgium – 11 February 1942, Baltimore, Maryland) was a Dutch mathematician.
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Eilenberg–Steenrod axioms
In mathematics, specifically in algebraic topology, the Eilenberg–Steenrod axioms are properties that homology theories of topological spaces have in common.
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Emmy Noether
Amalie Emmy NoetherEmmy is the Rufname, the second of two official given names, intended for daily use.
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Enumerative geometry
In mathematics, enumerative geometry is the branch of algebraic geometry concerned with counting numbers of solutions to geometric questions, mainly by means of intersection theory.
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Erlangen program
The Erlangen program is a method of characterizing geometries based on group theory and projective geometry.
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Ernst Steinitz
Ernst Steinitz (13 June 1871 – 29 September 1928) was a German mathematician.
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Euler characteristic
In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.
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Exotic sphere
In differential topology, an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean n-sphere.
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Exterior algebra
In mathematics, the exterior product or wedge product of vectors is an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogs.
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Factorization homology
In algebraic topology and category theory, factorization homology is a variant of topological chiral homology, motivated by an application to topological quantum field theory and cobordism hypothesis in particular.
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Felix Klein
Christian Felix Klein (25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group theory.
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Finite type invariant
In the mathematical theory of knots, a finite type invariant, or Vassiliev invariant, is a knot invariant that can be extended (in a precise manner to be described) to an invariant of certain singular knots that vanishes on singular knots with m + 1 singularities and does not vanish on some singular knot with 'm' singularities.
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Floer homology
In mathematics, Floer homology is a tool for studying symplectic geometry and low-dimensional topology.
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French mathematical seminars
French mathematical seminars have been an important type of institution combining research and exposition, active since the beginning of the twentieth century.
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Frobenius algebra
In mathematics, especially in the fields of representation theory and module theory, a Frobenius algebra is a finite-dimensional unital associative algebra with a special kind of bilinear form which gives the algebras particularly nice duality theories.
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Fukaya category
In symplectic topology, a discipline within mathematics, a Fukaya category of a symplectic manifold (M, \omega) is a category \mathcal F (M) whose objects are Lagrangian submanifolds of M, and morphisms are Floer chain groups: \mathrm (L_0, L_1).
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Functor
In mathematics, a functor is a map between categories.
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Fundamental class
In mathematics, the fundamental class is a homology class associated to an oriented manifold M of dimension n, which corresponds to the generator of the homology group H_n(M;\mathbf)\cong\mathbf.
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Fundamental group
In the mathematical field of algebraic topology, the fundamental group is a mathematical group associated to any given pointed topological space that provides a way to determine when two paths, starting and ending at a fixed base point, can be continuously deformed into each other.
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Gauss–Bonnet theorem
The Gauss–Bonnet theorem or Gauss–Bonnet formula in differential geometry is an important statement about surfaces which connects their geometry (in the sense of curvature) to their topology (in the sense of the Euler characteristic).
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Geometric topology
In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.
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Georges de Rham
Georges de Rham (10 September 1903 – 9 October 1990) was a Swiss mathematician, known for his contributions to differential topology.
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German Mathematical Society
The German Mathematical Society (Deutsche Mathematiker-Vereinigung – DMV) is the main professional society of German mathematicians.
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Glossary of algebraic topology
This is a glossary of properties and concepts in algebraic topology in mathematics.
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Glossary of category theory
This is a glossary of properties and concepts in category theory in mathematics.
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Graeme Segal
Graeme Bryce Segal FRS (born 21 December 1941) is an Australian mathematician, and professor at the University of Oxford.
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Grassmannian
In mathematics, the Grassmannian is a space which parametrizes all -dimensional linear subspaces of the n-dimensional vector space.
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Group action
In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.
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H-cobordism
In geometric topology and differential topology, an (n + 1)-dimensional cobordism W between n-dimensional manifolds M and N is an h-cobordism (the h stands for homotopy equivalence) if the inclusion maps are homotopy equivalences.
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Habilitation
Habilitation defines the qualification to conduct self-contained university teaching and is the key for access to a professorship in many European countries.
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Hamiltonian mechanics
Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics and predicts the same outcomes as non-Hamiltonian classical mechanics.
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Hassler Whitney
Hassler Whitney (March 23, 1907 – May 10, 1989) was an American mathematician.
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Hauptvermutung
The Hauptvermutung (German for main conjecture) of geometric topology is the conjecture that any two triangulations of a triangulable space have a common refinement, a single triangulation that is a subdivision of both of them.
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Hausdorff space
In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space in which distinct points have disjoint neighbourhoods.
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Heinrich Franz Friedrich Tietze
Heinrich Franz Friedrich Tietze (August 31, 1880 – February 17, 1964) was an Austrian mathematician, famous for the Tietze extension theorem on functions from topological spaces to the real numbers.
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Heinz Hopf
Heinz Hopf (19 November 1894 – 3 June 1971) was a German mathematician who worked on the fields of topology and geometry.
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Hellmuth Kneser
Hellmuth Kneser (16 April 1898 – 23 August 1973) was a Baltic German mathematician, who made notable contributions to group theory and topology.
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Helmut Hofer
Helmut Hermann W. Hofer (born February 18 or February 28, 1956) is a German-American mathematician, one of the founders of the area of symplectic topology.
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Henri Cartan
Henri Paul Cartan (July 8, 1904 – August 13, 2008) was a French mathematician with substantial contributions in algebraic topology.
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Henri Poincaré
Jules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.
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Henry Roy Brahana
Henry Roy Brahana (16 August 1895 in Lowell, Vermont – 15 October 1972 in Dennis, Massachusetts) was a mathematician, specializing in metabelian groups and related geometric structures.
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Hermann Grassmann
Hermann Günther Grassmann (Graßmann; April 15, 1809 – September 26, 1877) was a German polymath, known in his day as a linguist and now also as a mathematician.
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Hermann Künneth
Hermann Lorenz Künneth (July 6, 1892 Neustadt an der Haardt – May 7, 1975 Erlangen) was a German mathematician and renowned algebraic topologist, best known for his contribution to what is now known as the Künneth theorem.
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Hermann Weyl
Hermann Klaus Hugo Weyl, (9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher.
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Hilbert's axioms
Hilbert's axioms are a set of 20 assumptions proposed by David Hilbert in 1899 in his book Grundlagen der Geometrie (tr. The Foundations of Geometry) as the foundation for a modern treatment of Euclidean geometry.
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Hilbert's fifteenth problem
Hilbert's fifteenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert.
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Hilbert's fifth problem
Hilbert's fifth problem is the fifth mathematical problem from the problem list publicized in 1900 by mathematician David Hilbert, and concerns the characterization of Lie groups.
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Hilbert's third problem
The third on Hilbert's list of mathematical problems, presented in 1900, was the first to be solved.
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History of manifolds and varieties
The study of manifolds combines many important areas of mathematics: it generalizes concepts such as curves and surfaces as well as ideas from linear algebra and topology.
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Homogeneous space
In mathematics, particularly in the theories of Lie groups, algebraic groups and topological groups, a homogeneous space for a group G is a non-empty manifold or topological space X on which G acts transitively.
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Homological mirror symmetry
Homological mirror symmetry is a mathematical conjecture made by Maxim Kontsevich.
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Homology manifold
In mathematics, a homology manifold (or generalized manifold) is a locally compact topological space X that looks locally like a topological manifold from the point of view of homology theory.
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Homotopy
In topology, two continuous functions from one topological space to another are called homotopic (from Greek ὁμός homós "same, similar" and τόπος tópos "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions.
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Homotopy groups of spheres
In the mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other.
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Hopf algebra
In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously an (unital associative) algebra and a (counital coassociative) coalgebra, with these structures' compatibility making it a bialgebra, and that moreover is equipped with an antiautomorphism satisfying a certain property.
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Hyperbolic geometry
In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.
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Igor Frenkel
Igor Borisovich Frenkel (Игорь Борисович Френкель; born April 22, 1952) is a Russian-American mathematician at Yale University working in representation theory and mathematical physics.
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Implicit function theorem
In mathematics, more specifically in multivariable calculus, the implicit function theorem is a tool that allows relations to be converted to functions of several real variables.
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Intersection number
In mathematics, and especially in algebraic geometry, the intersection number generalizes the intuitive notion of counting the number of times two curves intersect to higher dimensions, multiple (more than 2) curves, and accounting properly for tangency.
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Intersection theory
In mathematics, intersection theory is a branch of algebraic geometry, where subvarieties are intersected on an algebraic variety, and of algebraic topology, where intersections are computed within the cohomology ring.
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Invariance of domain
Invariance of domain is a theorem in topology about homeomorphic subsets of Euclidean space Rn.
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J. H. C. Whitehead
John Henry Constantine Whitehead FRS (11 November 1904 – 8 May 1960), known as Henry, was a British mathematician and was one of the founders of homotopy theory.
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J. Peter May
Jon Peter May (born September 16, 1939 in New York) is an American mathematician, working in the fields of algebraic topology, category theory, homotopy theory, and the foundational aspects of spectra.
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Jacob Lurie
Jacob Alexander Lurie (born December 7, 1977) is an American mathematician who is a professor at Harvard University.
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James Harris Simons
James Harris "Jim" Simons (born April 25, 1938) is an American mathematician, billionaire hedge fund manager, and philanthropist.
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János Bolyai
János Bolyai (15 December 1802 – 27 January 1860) or Johann Bolyai, was a Hungarian mathematician, one of the founders of non-Euclidean geometry — a geometry that differs from Euclidean geometry in its definition of parallel lines.
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Jean Leray
Jean Leray (7 November 1906 – 10 November 1998) was a French mathematician, who worked on both partial differential equations and algebraic topology.
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Jean-Victor Poncelet
Jean-Victor Poncelet (1 July 1788 – 22 December 1867) was a French engineer and mathematician who served most notably as the Commanding General of the École Polytechnique.
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Joachim Lambek
Joachim "Jim" Lambek (5 December 1922 – 23 June 2014) was Peter Redpath Emeritus Professor of Pure Mathematics at McGill University, where he earned his Ph.D. degree in 1950 with Hans Zassenhaus as advisor.
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John C. Baez
John Carlos Baez (born June 12, 1961) is an American mathematical physicist and a professor of mathematics at the University of California, Riverside (UCR) in Riverside, California.
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John Horton Conway
John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.
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John Milnor
John Willard Milnor (born February 20, 1931) is an American mathematician known for his work in differential topology, K-theory and dynamical systems.
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Jones polynomial
In the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984.
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Joseph Bernstein
Joseph Bernstein (sometimes spelled I. N. Bernshtein; יוס(י)ף נאומוביץ ברנשטיין; Иосиф Наумович Бернштейн, Iosif Naumovič Bernštejn; born 18 April 1945) is an Israeli mathematician working at Tel Aviv University.
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Joseph Diez Gergonne
Joseph Diez Gergonne (19 June 1771 at Nancy, France – 4 May 1859 at Montpellier, France) was a French mathematician and logician.
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Journal of the American Mathematical Society
The Journal of the American Mathematical Society (JAMS), is a quarterly peer-reviewed mathematical journal published by the American Mathematical Society.
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Künneth theorem
In mathematics, especially in homological algebra and algebraic topology, a Künneth theorem, also called a Künneth formula, is a statement relating the homology of two objects to the homology of their product.
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Kenji Fukaya
Kenji Fukaya (Japanese: 深谷賢治, Fukaya Kenji, born March 12, 1959) is a Japanese mathematician known for his work in symplectic geometry and Riemannian geometry.
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Khovanov homology
In mathematics, Khovanov homology is an oriented link invariant that arises as the homology of a chain complex.
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Klein's encyclopedia
Klein's encyclopedia is a German mathematical encyclopedia published in six volumes from 1898 to 1933.
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Knot invariant
In the mathematical field of knot theory, a knot invariant is a quantity (in a broad sense) defined for each knot which is the same for equivalent knots.
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Knot polynomial
In the mathematical field of knot theory, a knot polynomial is a knot invariant in the form of a polynomial whose coefficients encode some of the properties of a given knot.
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Kontsevich invariant
In the mathematical theory of knots, the Kontsevich invariant, also known as the Kontsevich integral of an oriented framed link, is a universal Vassiliev invariant in the sense that any coefficient of the Kontsevich invariant is of a finite type, and conversely any finite type invariant can be presented as a linear combination of such coefficients.
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Kuranishi structure
In mathematics, especially in topology, a Kuranishi structure is a smooth analogue of scheme structure.
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L. E. J. Brouwer
Luitzen Egbertus Jan Brouwer (27 February 1881 – 2 December 1966), usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher, who worked in topology, set theory, measure theory and complex analysis.
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Langlands program
In mathematics, the Langlands program is a web of far-reaching and influential conjectures about connections between number theory and geometry.
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Leonhard Euler
Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.
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Leopold Vietoris
Leopold Vietoris (4 June 1891 – 9 April 2002) was an Austrian mathematician and a World War I veteran.
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Lie group
In mathematics, a Lie group (pronounced "Lee") is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.
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List of loop quantum gravity researchers
This is a list researchers in the physics field of loop quantum gravity.
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Local system
In mathematics, local coefficients is an idea from algebraic topology, a kind of half-way stage between homology theory or cohomology theory with coefficients in the usual sense, in a fixed abelian group A, and general sheaf cohomology which, roughly speaking, allows coefficients to vary from point to point in a topological space X. Such a concept was introduced by Norman Steenrod.
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Low-dimensional topology
In mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions.
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Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
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Marston Morse
Harold Calvin Marston Morse (March 24, 1892 – June 22, 1977) was an American mathematician best known for his work on the calculus of variations in the large, a subject where he introduced the technique of differential topology now known as Morse theory.
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Mathematical analysis
Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.
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Max Dehn
Max Wilhelm Dehn (November 13, 1878 – June 27, 1952) was a German-born American mathematician and student of David Hilbert.
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Maxim Kontsevich
Maxim Lvovich Kontsevich (Макси́м Льво́вич Конце́вич;; born 25 August 1964) is a Russian and French mathematician.
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Michael J. Hopkins
Michael Jerome Hopkins (born April 18, 1958) is an American mathematician known for work in algebraic topology.
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Michel Kervaire
Michel André Kervaire (26 April 1927 – 19 November 2007) was a French mathematician who made significant contributions to topology and algebra.
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Michio Jimbo
is a Japanese mathematician, currently a professor at the Rikkyo University.
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Mikhail Khovanov
Mikhail Khovanov (Михаил Хованов; born 1972) is a Russian-American professor of mathematics at Columbia University.
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Module (mathematics)
In mathematics, a module is one of the fundamental algebraic structures used in abstract algebra.
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Monoidal category
In mathematics, a monoidal category (or tensor category) is a category C equipped with a bifunctor that is associative up to a natural isomorphism, and an object I that is both a left and right identity for ⊗, again up to a natural isomorphism.
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Morse theory
"Morse function" redirects here.
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Natural transformation
In category theory, a branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal structure (i.e., the composition of morphisms) of the categories involved.
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Nicolai Reshetikhin
Nicolai Yuryevich Reshetikhin (Николай Юрьевич Решетихин, born October 10, 1958 in Leningrad, Soviet Union) is a mathematical physicist, currently a professor of mathematics at the University of California, Berkeley and a professor of mathematical physics at the University of Amsterdam.
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Non-Euclidean geometry
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean geometry.
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Norman Steenrod
Norman Earl Steenrod (April 22, 1910October 14, 1971) was a mathematician most widely known for his contributions to the field of algebraic topology.
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Oleg Viro
Oleg Yanovich Viro (Олег Янович Виро) (b. 13 May 1948, Leningrad, USSR) is a Russian mathematician in the fields of topology and algebraic geometry, most notably real algebraic geometry, tropical geometry and knot theory.
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Orbifold
In the mathematical disciplines of topology, geometry, and geometric group theory, an orbifold (for "orbit-manifold") is a generalization of a manifold.
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Orientability
In mathematics, orientability is a property of surfaces in Euclidean space that measures whether it is possible to make a consistent choice of surface normal vector at every point.
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Oswald Veblen
Oswald Veblen (June 24, 1880 – August 10, 1960) was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity.
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Otto Schreier
Otto Schreier (3 March 1901 in Vienna, Austria – 2 June 1929 in Hamburg, Germany) was an Austrian mathematician who made major contributions in combinatorial group theory and in the topology of Lie groups.
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Paul Koebe
Paul Koebe (15 February 1882 – 6 August 1945) was a 20th-century German mathematician.
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Peter J. Freyd
Peter J. Freyd (born February 5, 1936) is an American mathematician, a professor at the University of Pennsylvania, known for work in category theory and for founding the False Memory Syndrome Foundation.
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Peter Ozsváth
Peter Steven Ozsváth (born October 20, 1967) is a professor of mathematics at Princeton University.
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Piecewise linear manifold
In mathematics, a piecewise linear (PL) manifold is a topological manifold together with a piecewise linear structure on it.
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Pierre Ossian Bonnet
Pierre Ossian Bonnet (22 December 1819, Montpellier – 22 June 1892, Paris) was a French mathematician.
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Poincaré conjecture
In mathematics, the Poincaré conjecture is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space.
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Poincaré duality
In mathematics, the Poincaré duality theorem, named after Henri Poincaré, is a basic result on the structure of the homology and cohomology groups of manifolds.
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Poincaré–Hopf theorem
In mathematics, the Poincaré–Hopf theorem (also known as the Poincaré–Hopf index formula, Poincaré–Hopf index theorem, or Hopf index theorem) is an important theorem that is used in differential topology.
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Poisson manifold
In geometry, a Poisson structure on a smooth manifold M is a Lie bracket \ (called a Poisson bracket in this special case) on the algebra (M) of smooth functions on M, subject to the Leibniz rule Said in another manner, it is a Lie algebra structure on the vector space of smooth functions on M such that X_ \stackrel \: (M) \to (M) is a vector field for each smooth function f, which we call the Hamiltonian vector field associated to f. These vector fields span a completely integrable singular foliation, each of whose maximal integral sub-manifolds inherits a symplectic structure.
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Poul Heegaard
Poul Heegaard (November 2, 1871, Copenhagen - February 7, 1948, Oslo) was a Danish mathematician active in the field of topology.
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Projective geometry
Projective geometry is a topic in mathematics.
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Pseudogroup
In mathematics, a pseudogroup is an extension of the group concept, but one that grew out of the geometric approach of Sophus Lie, rather than out of abstract algebra (such as quasigroup, for example).
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Pseudomanifold
A pseudomanifold is a special type of topological space.
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Quantum field theory
In theoretical physics, quantum field theory (QFT) is the theoretical framework for constructing quantum mechanical models of subatomic particles in particle physics and quasiparticles in condensed matter physics.
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Quantum group
In mathematics and theoretical physics, the term quantum group denotes various kinds of noncommutative algebras with additional structure.
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Quantum invariant
In the mathematical field of knot theory, a quantum knot invariant or quantum invariant of a knot or link is a linear sum of colored Jones polynomial of surgery presentations of the knot complement.
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Quantum topology
Quantum topology is a branch of mathematics that connects quantum mechanics with low-dimensional topology.
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R-matrix
The term R-matrix has several meanings, depending on the field of study.
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Ramification (mathematics)
In geometry, ramification is 'branching out', in the way that the square root function, for complex numbers, can be seen to have two branches differing in sign.
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Real projective plane
In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface.
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René Thom
René Frédéric Thom (2 September 1923 – 25 October 2002) was a French mathematician.
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Ribbon category
In mathematics, a ribbon category, also called a tortile category, is a particular type of braided monoidal category.
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Richard Thomas (mathematician)
Richard Paul Winsley Thomas FRS is a British mathematician working in several areas of geometry.
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Riemann sphere
In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane, the complex plane plus a point at infinity.
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Riemann surface
In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold.
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Riemannian manifold
In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real, smooth manifold M equipped with an inner product g_p on the tangent space T_pM at each point p that varies smoothly from point to point in the sense that if X and Y are differentiable vector fields on M, then p \mapsto g_p(X(p),Y(p)) is a smooth function.
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Ronald Brown (mathematician)
Ronald Brown is an English mathematician.
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Ross Street
Ross Howard Street (29 September 1945, Sydney &ndash) is an Australian mathematician specialising in category theory.
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Ruth Lawrence
Ruth Elke Lawrence-Neimark (רות אלקה לורנס-נאימרק, born 2 August 1971) is a British–Israeli mathematician and an associate professor of mathematics at the Einstein Institute of Mathematics, Hebrew University of Jerusalem, and a researcher in knot theory and algebraic topology.
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Samuel Eilenberg
Samuel Eilenberg (September 30, 1913 – January 30, 1998) was a Polish-born American mathematician who co-founded category theory with Saunders Mac Lane.
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Saunders Mac Lane
Saunders Mac Lane (4 August 1909 – 14 April 2005) was an American mathematician who co-founded category theory with Samuel Eilenberg.
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Schubert calculus
In mathematics, Schubert calculus is a branch of algebraic geometry introduced in the nineteenth century by Hermann Schubert, in order to solve various counting problems of projective geometry (part of enumerative geometry).
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Second-countable space
In topology, a second-countable space, also called a completely separable space, is a topological space whose topology has a countable base.
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Sheaf (mathematics)
In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space.
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Sheaf cohomology
In mathematics, sheaf cohomology is the application of homological algebra to analyze the global sections of a sheaf on a topological space.
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Shiing-Shen Chern
Shiing-Shen Chern (October 26, 1911 – December 3, 2004) was a Chinese-American mathematician who made fundamental contributions to differential geometry and topology.
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Simon Donaldson
Sir Simon Kirwan Donaldson FRS (born 20 August 1957), is an English mathematician known for his work on the topology of smooth (differentiable) four-dimensional manifolds and Donaldson–Thomas theory.
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Simplicial homology
In algebraic topology, simplicial homology formalizes the idea of the number of holes of a given dimension in a simplicial complex.
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Simplicial polytope
In geometry, a simplicial polytope is a polytope whose facets are all simplices.
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Simplicial set
In mathematics, a simplicial set is an object made up of "simplices" in a specific way.
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Simply connected space
In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the space) into any other such path while preserving the two endpoints in question.
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Singular homology
In algebraic topology, a branch of mathematics, singular homology refers to the study of a certain set of algebraic invariants of a topological space X, the so-called homology groups H_n(X).
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Skein relation
Skein relations are a mathematical tool used to study knots.
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Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
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Snake lemma
The snake lemma is a tool used in mathematics, particularly homological algebra, to construct long exact sequences.
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Solomon Lefschetz
Solomon Lefschetz (Соломо́н Ле́фшец; 3 September 1884 – 5 October 1972) was an American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equations.
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Sophus Lie
Marius Sophus Lie (17 December 1842 – 18 February 1899) was a Norwegian mathematician.
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Spectral sequence
In homological algebra and algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations.
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Spherical category
In category theory, a branch of mathematics, a spherical category is a pivotal category (a monoidal category with traces) in which left and right traces coincide.
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Steenrod problem
In mathematics, and particularly homology theory, Steenrod's Problem (named after mathematician Norman Steenrod) is a problem concerning the realisation of homology classes by singular manifolds.
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Stephen Smale
Stephen Smale (born July 15, 1930) is an American mathematician from Flint, Michigan.
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String diagram
In category theory, string diagrams are a way of representing morphisms in monoidal categories, or more generally 2-cells in 2-categories.
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String topology
String topology, a branch of mathematics, is the study of algebraic structures on the homology of free loop spaces.
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Symmetric space
In differential geometry, representation theory and harmonic analysis, a symmetric space is a pseudo-Riemannian manifold whose group of symmetries contains an inversion symmetry about every point.
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Tangle (mathematics)
In mathematics, a tangle is generally one of two related concepts.
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Temperley–Lieb algebra
In statistical mechanics, the Temperley–Lieb algebra is an algebra from which are built certain transfer matrices, invented by Neville Temperley and Elliott Lieb.
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Thom space
In mathematics, the Thom space, Thom complex, or Pontryagin–Thom construction (named after René Thom and Lev Pontryagin) of algebraic topology and differential topology is a topological space associated to a vector bundle, over any paracompact space.
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Tibor Radó
Tibor Radó (June 2, 1895 – December 29, 1965) was a Hungarian mathematician who moved to the United States after World War I.
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Topological group
In mathematics, a topological group is a group G together with a topology on G such that the group's binary operation and the group's inverse function are continuous functions with respect to the topology.
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Topological manifold
In topology, a branch of mathematics, a topological manifold is a topological space (which may also be a separated space) which locally resembles real n-dimensional space in a sense defined below.
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Topological modular forms
In mathematics, topological modular forms (tmf) is the name of a spectrum that describes a generalized cohomology theory.
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Topological quantum field theory
A topological quantum field theory (or topological field theory or TQFT) is a quantum field theory which computes topological invariants.
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Topological space
In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.
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Topological string theory
In theoretical physics, topological string theory is a version of string theory.
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Triangulation (geometry)
In geometry, a triangulation is a subdivision of a planar object into triangles, and by extension the subdivision of a higher-dimension geometric object into simplices.
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Ulisse Dini
Ulisse Dini (14 November 1845 – 28 October 1918) was an Italian mathematician and politician, born in Pisa.
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Uniformization theorem
In mathematics, the uniformization theorem says that every simply connected Riemann surface is conformally equivalent to one of the three Riemann surfaces: the open unit disk, the complex plane, or the Riemann sphere.
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Vaughan Jones
Sir Vaughan Frederick Randal Jones (born 31 December 1952) is a New Zealand and American mathematician, known for his work on von Neumann algebras and knot polynomials.
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Vladimir Drinfeld
Vladimir Gershonovich Drinfeld (Володи́мир Ге́ршонович Дрінфельд; Влади́мир Ге́ршонович Дри́нфельд; born February 14, 1954), surname also romanized as Drinfel'd, is a Ukrainian-American mathematician, currently working at the University of Chicago.
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Vladimir Turaev
Vladimir Georgievich Turaev (Владимир Георгиевич Тураев, born 17 October 1954) is a Russian mathematician, specializing in topology.
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Whitney embedding theorem
In mathematics, particularly in differential topology, there are two Whitney embedding theorems, named after Hassler Whitney.
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Wigner–Weyl transform
In quantum mechanics, the Wigner–Weyl transform or Weyl–Wigner transform is the invertible mapping between functions in the quantum phase space formulation and Hilbert space operators in the Schrödinger picture.
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Witold Hurewicz
Witold Hurewicz (June 29, 1904 – September 6, 1956) was a Jewish-Polish mathematician.
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Yakov Eliashberg
Yakov Eliashberg (Яков Матвеевич Элиашберг; born 11 December 1946) is an American mathematician who was born in Leningrad, USSR.
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Zero of a function
In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).
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Zoltán Szabó (mathematician)
Zoltán Szabó (born on November 24, 1965) is a professor of mathematics at Princeton University.
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5-manifold
In mathematics, a 5-manifold is a 5-dimensional topological manifold, possibly with a piecewise linear or smooth structure.
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References
[1] https://en.wikipedia.org/wiki/Timeline_of_manifolds
