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19 relations: Atlas (topology), Cardinality of the continuum, Casson handle, Clifford Taubes, Cobordism, Diffeomorphism, Differentiable manifold, Differential structure, Euclidean space, Exotic sphere, Generalized Poincaré conjecture, Graduate Studies in Mathematics, H-cobordism, Homeomorphism, Mathematics, Michael Freedman, N-sphere, Simon Donaldson, Smooth structure.
Atlas (topology)
In mathematics, particularly topology, one describes a manifold using an atlas.
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Cardinality of the continuum
In set theory, the cardinality of the continuum is the cardinality or “size” of the set of real numbers \mathbb R, sometimes called the continuum.
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Casson handle
In 4-dimensional topology, a branch of mathematics, a Casson handle is a 4-dimensional topological 2-handle constructed by an infinite procedure.
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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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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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Diffeomorphism
In mathematics, a diffeomorphism is an isomorphism of smooth manifolds.
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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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Differential structure
In mathematics, an n-dimensional differential structure (or differentiable structure) on a set M makes M into an n-dimensional differential manifold, which is a topological manifold with some additional structure that allows for differential calculus on the manifold.
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Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
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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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Generalized Poincaré conjecture
In the mathematical area of topology, the Generalized Poincaré conjecture is a statement that a manifold which is a homotopy sphere 'is' a sphere.
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Graduate Studies in Mathematics
Graduate Studies in Mathematics (GSM) is a series of graduate-level textbooks in mathematics published by the American Mathematical Society (AMS).
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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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Homeomorphism
In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.
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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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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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N-sphere
In mathematics, the n-sphere is the generalization of the ordinary sphere to spaces of arbitrary dimension.
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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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Smooth structure
In mathematics, a smooth structure on a manifold allows for an unambiguous notion of smooth function.
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