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35 relations: Barry Mazur, Cobordism, Dennis Barden, Differentiable manifold, Differential topology, Fields Medal, Generalized Poincaré conjecture, Geometric topology, Grigori Perelman, Groupoid, Handle decomposition, Hassler Whitney, Henri Poincaré, Homotopy, John Milnor, John R. Stallings, Manifold, Michael Freedman, Millennium Prize Problems, Piecewise linear manifold, Poincaré conjecture, Princeton University Press, Principal homogeneous space, Ricci flow, Richard S. Hamilton, Semi-s-cobordism, Simon Donaldson, Simple-homotopy equivalence, Simply connected space, Smooth structure, Springer Science+Business Media, Stephen Smale, Topological manifold, Whitehead torsion, Whitney embedding theorem.
Barry Mazur
Barry Charles Mazur (born December 19, 1937) is an American mathematician and a Gerhard Gade University Professor at Harvard University.
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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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Dennis Barden
Dennis Barden is a mathematician at the University of Cambridge working in the fields of geometry and topology.
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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 topology
In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds.
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Fields Medal
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years.
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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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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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Grigori Perelman
Grigori Yakovlevich Perelman (a; born 13 June 1966) is a Russian mathematician.
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Groupoid
In mathematics, especially in category theory and homotopy theory, a groupoid (less often Brandt groupoid or virtual group) generalises the notion of group in several equivalent ways.
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Handle decomposition
In mathematics, a handle decomposition of an m-manifold M is a union where each M_i is obtained from M_ by the attaching of i-handles.
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Hassler Whitney
Hassler Whitney (March 23, 1907 – May 10, 1989) was an American mathematician.
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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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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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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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John R. Stallings
John Robert Stallings Jr. (July 22, 1935 – November 24, 2008) was a mathematician known for his seminal contributions to geometric group theory and 3-manifold topology.
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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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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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Millennium Prize Problems
The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000.
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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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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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Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University.
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Principal homogeneous space
In mathematics, a principal homogeneous space, or torsor, for a group G is a homogeneous space X for G in which the stabilizer subgroup of every point is trivial.
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Ricci flow
In differential geometry, the Ricci flow (Italian) is an intrinsic geometric flow.
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Richard S. Hamilton
Richard Streit Hamilton (born 1943) is Davies Professor of Mathematics at Columbia University.
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Semi-s-cobordism
In mathematics, a cobordism (W, M, M&minus) of an (n + 1)-dimensionsal manifold (with boundary) W between its boundary components, two n-manifolds M and M−, is called a semi-s-cobordism if (and only if) the inclusion M \hookrightarrow W is a simple homotopy equivalence (as in an ''s''-cobordism) but the inclusion M^- \hookrightarrow W is not a homotopy equivalence at all.
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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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Simple-homotopy equivalence
In mathematics, particularly the area of topology, a simple-homotopy equivalence is a refinement of the concept of homotopy equivalence.
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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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Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
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Stephen Smale
Stephen Smale (born July 15, 1930) is an American mathematician from Flint, Michigan.
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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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Whitehead torsion
In geometric topology, a field within mathematics, the obstruction to a homotopy equivalence f\colon X \to Y of finite CW-complexes being a simple homotopy equivalence is its Whitehead torsion \tau(f) which is an element in the Whitehead group \operatorname(\pi_1(Y)).
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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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Cobordism theorem, H cobordism, H-Cobordism, H-Cobordism theorem, H-cobordism theorem, S-Cobordism theorem, S-cobordism, S-cobordism theorem, Smale h-cobordism theorem, Smale's h-cobordism theorem, Smale's theorem.
References
[1] https://en.wikipedia.org/wiki/H-cobordism
