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40 relations: American Mathematical Society, Arf invariant, Armand Borel, Atiyah–Singer index theorem, Cahit Arf, Cambridge University Press, Casson invariant, Cohomology, Compact space, Differentiable manifold, E8 manifold, Enriques surface, Friedrich Hirzebruch, Genus of a multiplicative sequence, Hirzebruch signature theorem, Homology sphere, Homotopy groups of spheres, Intersection form (4-manifold), Isadore Singer, John Milnor, K3 surface, Kirby–Siebenmann class, Manifold, Mazur manifold, Michael Atiyah, Michael Freedman, Michel Kervaire, Poincaré duality, Princeton University Press, Quadratic form, Robion Kirby, Signature (topology), Simply connected space, Smooth structure, Spin structure, Stiefel–Whitney class, Topological manifold, Torsion (algebra), Unimodular lattice, Vladimir Abramovich Rokhlin.
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
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Arf invariant
In mathematics, the Arf invariant of a nonsingular quadratic form over a field of characteristic 2 was defined by Turkish mathematician when he started the systematic study of quadratic forms over arbitrary fields of characteristic 2.
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Armand Borel
Armand Borel (21 May 1923 – 11 August 2003) was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993.
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Atiyah–Singer index theorem
In differential geometry, the Atiyah–Singer index theorem, proved by, states that for an elliptic differential operator on a compact manifold, the analytical index (related to the dimension of the space of solutions) is equal to the topological index (defined in terms of some topological data).
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Cahit Arf
Cahit Arf (11 October 1910 – 26 December 1997) was a Turkish mathematician.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Casson invariant
In 3-dimensional topology, a part of the mathematical field of geometric topology, the Casson invariant is an integer-valued invariant of oriented integral homology 3-spheres, introduced by Andrew Casson.
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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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Compact space
In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).
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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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E8 manifold
In mathematics, the E8 manifold is the unique compact, simply connected topological 4-manifold with intersection form the ''E''8 lattice.
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Enriques surface
In mathematics, Enriques surfaces are algebraic surfaces such that the irregularity q.
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Friedrich Hirzebruch
Friedrich Ernst Peter Hirzebruch ForMemRS (17 October 1927 – 27 May 2012) was a German mathematician, working in the fields of topology, complex manifolds and algebraic geometry, and a leading figure in his generation.
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Genus of a multiplicative sequence
In mathematics, the genus of a sequence is a ring homomorphism, from the ring of smooth compact manifolds to another ring, usually the ring of rational numbers.
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Hirzebruch signature theorem
In differential topology, an area of mathematics, the Hirzebruch signature theorem (sometimes called the Hirzebruch index theorem) is Friedrich Hirzebruch's 1954 result expressing the signature of a smooth compact oriented manifold by a linear combination of Pontryagin numbers called the L-genus.
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Homology sphere
In algebraic topology, a homology sphere is an n-manifold X having the homology groups of an n-sphere, for some integer n ≥ 1.
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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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Intersection form (4-manifold)
In mathematics, the intersection form of an oriented compact 4-manifold is a special symmetric bilinear form on the 2nd cohomology group of the 4-manifold.
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Isadore Singer
Isadore Manuel Singer (born May 3, 1924) is an American mathematician.
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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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K3 surface
In mathematics, a K3 surface is a complex or algebraic smooth minimal complete surface that is regular and has trivial canonical bundle.
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Kirby–Siebenmann class
In mathematics, the Kirby–Siebenmann class is an element of the fourth cohomology group which must vanish if a topological manifold M is to have a piecewise linear structure.
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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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Mazur manifold
In differential topology, a branch of mathematics, a Mazur manifold is a contractible, compact, smooth 4-dimensional manifold (with boundary) which is not diffeomorphic to the standard 4-ball.
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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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Michael Freedman
Michael Hartley Freedman (born 21 April 1951) is an American mathematician, at Microsoft Station Q, a research group at the University of California, Santa Barbara.
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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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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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Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University.
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Quadratic form
In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables.
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Robion Kirby
Robion Cromwell Kirby (born February 25, 1938) is a Professor of Mathematics at the University of California, Berkeley who specializes in low-dimensional topology.
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Signature (topology)
In the mathematical field of topology, the signature is an integer invariant which is defined for an oriented manifold M of dimension d.
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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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Smooth structure
In mathematics, a smooth structure on a manifold allows for an unambiguous notion of smooth function.
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Spin structure
In differential geometry, a spin structure on an orientable Riemannian manifold allows one to define associated spinor bundles, giving rise to the notion of a spinor in differential geometry.
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Stiefel–Whitney class
In mathematics, in particular in algebraic topology and differential geometry, the Stiefel–Whitney classes are a set of topological invariants of a real vector bundle that describe the obstructions to constructing everywhere independent sets of sections of the vector bundle.
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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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Torsion (algebra)
In abstract algebra, the term torsion refers to elements of finite order in groups and to elements of modules annihilated by regular elements of a ring.
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Unimodular lattice
In geometry and mathematical group theory, a unimodular lattice is an integral lattice of determinant 1 or −1.
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Vladimir Abramovich Rokhlin
Vladimir Abramovich Rokhlin (Russian: Влади́мир Абра́мович Ро́хлин) (23 August 1919 – 3 December 1984) was a Soviet mathematician, who made numerous contributions in algebraic topology, geometry, measure theory, probability theory, ergodic theory and entropy theory.
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Freedman-Kirby theorem, Kervaire-Milnor formula, Kervaire-Milnor theorem, Kervaire–Milnor formula, Rochlin invariant, Rochlin theorem, Rochlin's theorem, Rohlin invariant, Rohlin's theorem, Rokhlin invariant, Rokhlin theorem.
References
[1] https://en.wikipedia.org/wiki/Rokhlin's_theorem
