Get it on Google Play
New! Download Unionpedia on your Android™ device!
Faster access than browser!


Index 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. [1]

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.

New!!: H-cobordism and Barry Mazur · See more »


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.

New!!: H-cobordism and Cobordism · See more »

Dennis Barden

Dennis Barden is a mathematician at the University of Cambridge working in the fields of geometry and topology.

New!!: H-cobordism and Dennis Barden · See more »

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.

New!!: H-cobordism and Differentiable manifold · See more »

Differential topology

In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds.

New!!: H-cobordism and Differential topology · See more »

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.

New!!: H-cobordism and Fields Medal · See more »

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.

New!!: H-cobordism and Generalized Poincaré conjecture · See more »

Geometric topology

In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.

New!!: H-cobordism and Geometric topology · See more »

Grigori Perelman

Grigori Yakovlevich Perelman (a; born 13 June 1966) is a Russian mathematician.

New!!: H-cobordism and Grigori Perelman · See more »


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.

New!!: H-cobordism and Groupoid · See more »

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.

New!!: H-cobordism and Handle decomposition · See more »

Hassler Whitney

Hassler Whitney (March 23, 1907 – May 10, 1989) was an American mathematician.

New!!: H-cobordism and Hassler Whitney · See more »

Henri Poincaré

Jules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.

New!!: H-cobordism and Henri Poincaré · See more »


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.

New!!: H-cobordism and Homotopy · See more »

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.

New!!: H-cobordism and John Milnor · See more »

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.

New!!: H-cobordism and John R. Stallings · See more »


In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

New!!: H-cobordism and Manifold · See more »

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.

New!!: H-cobordism and Michael Freedman · See more »

Millennium Prize Problems

The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000.

New!!: H-cobordism and Millennium Prize Problems · See more »

Piecewise linear manifold

In mathematics, a piecewise linear (PL) manifold is a topological manifold together with a piecewise linear structure on it.

New!!: H-cobordism and Piecewise linear manifold · See more »

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.

New!!: H-cobordism and Poincaré conjecture · See more »

Princeton University Press

Princeton University Press is an independent publisher with close connections to Princeton University.

New!!: H-cobordism and Princeton University Press · See more »

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.

New!!: H-cobordism and Principal homogeneous space · See more »

Ricci flow

In differential geometry, the Ricci flow (Italian) is an intrinsic geometric flow.

New!!: H-cobordism and Ricci flow · See more »

Richard S. Hamilton

Richard Streit Hamilton (born 1943) is Davies Professor of Mathematics at Columbia University.

New!!: H-cobordism and Richard S. Hamilton · See more »


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.

New!!: H-cobordism and Semi-s-cobordism · See more »

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.

New!!: H-cobordism and Simon Donaldson · See more »

Simple-homotopy equivalence

In mathematics, particularly the area of topology, a simple-homotopy equivalence is a refinement of the concept of homotopy equivalence.

New!!: H-cobordism and Simple-homotopy equivalence · See more »

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.

New!!: H-cobordism and Simply connected space · See more »

Smooth structure

In mathematics, a smooth structure on a manifold allows for an unambiguous notion of smooth function.

New!!: H-cobordism and Smooth structure · See more »

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.

New!!: H-cobordism and Springer Science+Business Media · See more »

Stephen Smale

Stephen Smale (born July 15, 1930) is an American mathematician from Flint, Michigan.

New!!: H-cobordism and Stephen Smale · See more »

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.

New!!: H-cobordism and Topological manifold · See more »

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)).

New!!: H-cobordism and Whitehead torsion · See more »

Whitney embedding theorem

In mathematics, particularly in differential topology, there are two Whitney embedding theorems, named after Hassler Whitney.

New!!: H-cobordism and Whitney embedding theorem · See more »

Redirects here:

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.


[1] https://en.wikipedia.org/wiki/H-cobordism

Hey! We are on Facebook now! »