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55 relations: Algebraic geometry, Almost complex manifold, Atiyah–Bott fixed-point theorem, Cambridge University Press, Chern class, Clifford Taubes, Closed manifold, Cohomology, Cokernel, Cup product, Donaldson theory, Donaldson–Thomas theory, Edward Witten, Elementary particle, Euler class, Floer homology, Fundamental class, General relativity, Generating function, Genus (mathematics), Gopakumar–Vafa invariant, Helmholtz free energy, Homology (mathematics), Intersection theory, Invariant (mathematics), Kähler manifold, Künneth theorem, Kuranishi structure, Linearization, Mathematics, Measure (mathematics), Michael Atiyah, Mikhail Leonidovich Gromov, Moduli of algebraic curves, Moduli space, Orbifold, Path integral formulation, Pseudoholomorphic curve, Quantum cohomology, Quantum mechanics, Raoul Bott, Rational number, Scheme (mathematics), Seiberg–Witten invariants, Stable map, String (physics), String theory, Surjective function, Symplectic geometry, Symplectic manifold, ..., Taubes's Gromov invariant, Topological string theory, Toric variety, Type II string theory, Vector bundle. Expand index (5 more) »
Algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.
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Almost complex manifold
In mathematics, an almost complex manifold is a smooth manifold equipped with a smooth linear complex structure on each tangent space.
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Atiyah–Bott fixed-point theorem
In mathematics, the Atiyah–Bott fixed-point theorem, proven by Michael Atiyah and Raoul Bott in the 1960s, is a general form of the Lefschetz fixed-point theorem for smooth manifolds M, which uses an elliptic complex on M. This is a system of elliptic differential operators on vector bundles, generalizing the de Rham complex constructed from smooth differential forms which appears in the original Lefschetz fixed-point theorem.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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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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Clifford Taubes
Clifford Henry Taubes (born 1954) is the William Petschek Professor of Mathematics at Harvard University and works in gauge field theory, differential geometry, and low-dimensional topology.
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Closed manifold
In mathematics, a closed manifold is a type of topological space, namely a compact manifold without boundary.
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Cohomology
In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups associated to a topological space, often defined from a cochain complex.
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Cokernel
In mathematics, the cokernel of a linear mapping of vector spaces f: X → Y is the quotient space Y/im(f) of the codomain of f by the image of f. The dimension of the cokernel is called the corank of f. Cokernels are dual to the kernels of category theory, hence the name: the kernel is a subobject of the domain (it maps to the domain), while the cokernel is a quotient object of the codomain (it maps from the codomain).
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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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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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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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Elementary particle
In particle physics, an elementary particle or fundamental particle is a particle with no substructure, thus not composed of other particles.
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Euler class
In mathematics, specifically in algebraic topology, the Euler class is a characteristic class of oriented, real vector bundles.
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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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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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General relativity
General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.
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Generating function
In mathematics, a generating function is a way of encoding an infinite sequence of numbers (an) by treating them as the coefficients of a power series.
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Genus (mathematics)
In mathematics, genus (plural genera) has a few different, but closely related, meanings.
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Gopakumar–Vafa invariant
In theoretical physics Rajesh Gopakumar and Cumrun Vafa introduced new topological invariants, which named Gopakumar–Vafa invariant, that represent the number of BPS states on Calabi–Yau 3-fold, in a series of papers.
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Helmholtz free energy
In thermodynamics, the Helmholtz free energy is a thermodynamic potential that measures the useful work obtainable from a closed thermodynamic system at a constant temperature and volume.
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Homology (mathematics)
In mathematics, homology is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces.
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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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Invariant (mathematics)
In mathematics, an invariant is a property, held by a class of mathematical objects, which remains unchanged when transformations of a certain type are applied to the objects.
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Kähler manifold
In mathematics and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a Riemannian structure, and a symplectic structure.
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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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Kuranishi structure
In mathematics, especially in topology, a Kuranishi structure is a smooth analogue of scheme structure.
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Linearization
In mathematics, linearization is finding the linear approximation to a function at a given point.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Measure (mathematics)
In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size.
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Michael Atiyah
Sir Michael Francis Atiyah (born 22 April 1929) is an English mathematician specialising in geometry.
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Mikhail Leonidovich Gromov
Mikhail Leonidovich Gromov (also Mikhael Gromov, Michael Gromov or Mischa Gromov; Михаи́л Леони́дович Гро́мов; born 23 December 1943), is a French-Russian mathematician known for work in geometry, analysis and group theory.
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Moduli of algebraic curves
In algebraic geometry, a moduli space of (algebraic) curves is a geometric space (typically a scheme or an algebraic stack) whose points represent isomorphism classes of algebraic curves.
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Moduli space
In algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects.
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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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Path integral formulation
The path integral formulation of quantum mechanics is a description of quantum theory that generalizes the action principle of classical mechanics.
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Pseudoholomorphic curve
In mathematics, specifically in topology and geometry, a pseudoholomorphic curve (or J-holomorphic curve) is a smooth map from a Riemann surface into an almost complex manifold that satisfies the Cauchy–Riemann equation.
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Quantum cohomology
In mathematics, specifically in symplectic topology and algebraic geometry, a quantum cohomology ring is an extension of the ordinary cohomology ring of a closed symplectic manifold.
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Quantum mechanics
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
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Raoul Bott
Raoul Bott, (September 24, 1923 – December 20, 2005) was a Hungarian-American mathematician known for numerous basic contributions to geometry in its broad sense.
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Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.
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Scheme (mathematics)
In mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x.
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Seiberg–Witten invariants
In mathematics, Seiberg–Witten invariants are invariants of compact smooth 4-manifolds introduced by, using the Seiberg–Witten theory studied by during their investigations of Seiberg–Witten gauge theory.
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Stable map
In mathematics, specifically in symplectic topology and algebraic geometry, one can construct the moduli space of stable maps, satisfying specified conditions, from Riemann surfaces into a given symplectic manifold.
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String (physics)
In physics, a string is a physical phenomenon that appears in string theory and related subjects.
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String theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings.
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Surjective function
In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x).
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Symplectic geometry
Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form.
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Symplectic manifold
In mathematics, a symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2-form, ω, called the symplectic form.
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Taubes's Gromov invariant
In mathematics, the Gromov invariant of Clifford Taubes counts embedded (possibly disconnected) pseudoholomorphic curves in a symplectic 4-manifold, where the curves are holomorphic with respect to an auxiliary compatible almost complex structure.
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Topological string theory
In theoretical physics, topological string theory is a version of string theory.
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Toric variety
In algebraic geometry, a toric variety or torus embedding is an algebraic variety containing an algebraic torus as an open dense subset, such that the action of the torus on itself extends to the whole variety.
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Type II string theory
In theoretical physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings theories.
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Vector bundle
In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X (for example X could be a topological space, a manifold, or an algebraic variety): to every point x of the space X we associate (or "attach") a vector space V(x) in such a way that these vector spaces fit together to form another space of the same kind as X (e.g. a topological space, manifold, or algebraic variety), which is then called a vector bundle over X.
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Gromov witten, Gromov-Witten invariant, Gromov-Witten invariants, Gromov-Witten theory, Gromov-Witten-invariants, Gromov–Witten invariants, Gromov–Witten theory, Relative Gromov-Witten invariant, Relative Gromov–Witten invariant.
References
[1] https://en.wikipedia.org/wiki/Gromov–Witten_invariant
