If is a Simply Connected, Compact Manifold with a boundary that has two components, and , such that inclusion of each is a Homotopy equivalence, then is Diffeomorphic to the product for . In other words, if and are two simply connected Manifolds 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 theorem is the Poincaré Conjecture in dimension . Smale proved this theorem in 1961.
See also Diffeomorphism, Poincaré Conjecture, Surgery
Smale, S. ``Generalized Poincaré's Conjecture in Dimensions Greater than Four.'' Ann. Math. 74, 391-406, 1961.