Poincare and h-cobordism theorem

The way to define an h-cobordism is as follows: if the inclusion maps $\iota_{0}$ and $\iota_{1}$ corresponding to a cobordism $M$ are homotopy equivalences, then $M$ is said to be an h-cobordism. That is, if the inclusion maps $\iota_{0}:N_{0}\hookrightarrow M$ and $\iota_{1}: N_{1}\hookrightarrow M$ are homotopy equivalences, then we say that the cobordism $M$ is an h-cobordism. The h-cobordism theorem is as follows:

Theorem (h-cobordism theorem): Let $M$ be a simply connected smooth compact $N$ h-cobordism between a pair $(B_{0}, B_{1})$ that are $N-1$ manifolds. In $N\geq 6$, there exists a diffeomorphism between the product $B_{0}\times [0, 1]$ and $M$.

In this case, our attention is on the $N\geq 6$ case, which for the moment we will consider as a version of the Poincare conjecture. In terms of homotopy to the $N-$Sphere, the Poincare conjecture in our setting can be rewritten. How does one work this out? This is a beautiful result by Smale, which is an outline of the Poincare conjecture itself in this setting. The statement, with a proof that can be written rather naively is as follows:

Poincare conjecture in $N\geq 6$: For a smooth manifold with homotopy-equivalence to the $N-$Sphere, there exists a homeomorphism to the $N-$Sphere.

Proof: Well the proof is slightly non-trivial to write it out here. Check the notes for a quick look at this.