Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. A connection between two manifolds of the same dimension n. via a manifold of dimension , where the smaller manifolds are included in the boundary of the larger manifold.
 n. The theory and study of such objects.
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The basis of topological quantum field theories and spin foam models are in functors that relate these cobordism categories to categories of representations of quantum groups.

This morning Jacob Lurie posted a draft of an expository paper on his work (with Mike Hopkins) classifying extended (infinity, n)  categorical topological field theories and their relation to the BaezDolan cobordism hypothesis.

Any senioryear college student who is majoring in mathematics should be able to prove the was proved by Steve Smale in 1961 with his hcobordism theorem, for which he won a was proved in 1981 by Michael Freedman with his theorem on Casson handles, for which he shared a Fields medal with Andrew Casson, who had pioneered study in this area.

Unfortunately, the socalled "Whitney trick" which allowed the cobordism theorems of the late 20th century to produce such breakthroughs in topology is not possible in three dimensions, leaving Poincare's original formulation of the conjecture open.

Freedman's theorem was essentially a strengthening of the results of Smale's cobordism theorem, obtained at the expense of weakening the premises.

Any senioryear college student who is majoring in mathematics should be able to prove the was proved by Steve Smale in 1961 with his hcobordism theorem, for which he won a was proved in 1981 by M. Freedman with his theorem on Casson handles, for which he shared a Fields medal with A Casson, who had pioneered study in this area.

In cobordism theory, he gave his name to the PontryaginThom construction.

Pontryagin classes (related to Chern classes), Pontryagin spaces, Pontryagin duality, and study cobordism theory?

n \geq 5 \ was proved by Steve Smale in 1961 with his hcobordism theorem, for which he won a [[Fields Medal]].

The page states that "the hcobordism theorem actually demonstrates that a diffeomorphism exists for n >
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