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.

**References**

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

© 1996-9

1999-05-25