h-cobordism theorem

The h-cobordism theorem (due to Smale 1962) and the s-cobordism theorem provide sufficient conditions for an h-cobordism to be isomorphic to a cylinder. There are famous counterexamples where the h-cobordism theorem fails (in the smooth category) and h-cobordisms exist which are not isomorphic to a cylinder. These counterexamples arise specifically in the case of 5-dimensional cobordisms between 4-dimensional boundaries. The most prominent example involves the topological manifold known as the..