“h-Cobordism Theorem”的概念、定义、习题解题方法及翻译-数学辞典

单词

h-Cobordism Theorem

释义

h-Cobordism Theorem

If is a Simply Connected, Compact Manifold with a boundary that has two components, and , suchthat inclusion of each is a Homotopy equivalence, then is Diffeomorphic to the product for . In other words, if and are two simply connectedManifolds of Dimension and there exists an h-Cobordism between them, then is a product and is Diffeomorphic to .

The proof of the -cobordism theorem can be accomplished using Surgery. A particular case of the -cobordism theoremis the Poincaré Conjecture in dimension . Smale proved this theorem in 1961.

See also Diffeomorphism, Poincaré Conjecture, Surgery

References

Smale, S. ``Generalized Poincaré's Conjecture in Dimensions Greater than Four.'' Ann. Math. 74, 391-406, 1961.

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