A Classical Technique to Prove the h-Cobordism Theorem

Let W be an m dimensional compact smooth manifold with boundary ∂W = ∂_ W ⊔ ∂+W, where submanifolds ∂_ W and ∂+W are closed and disjoint. Then suppose that W, ∂_W, and ∂ +W are all simply connected, dim W ≥ 6, and H*(W, ∂_W) = 0. The h-Cobordism Theorem states that W is diffeormorphic to a product cobordism.;In this paper we will follow a classical technique developed by John Milnor in his "Lectures on the h-Cobordism Theorem" half a century ago.