H-Cobordism Theorem

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Theorem

Let $X^n, Y^n$ be two simply connected manifolds.

Let $n \in \N: n \ge 5$ and $\exists W$ such that $W$ is an h-cobordism between $X$ and $Y$.


Then $\exists \psi: W \to X \times \left[{0 \,.\,.\, 1}\right]$ such that $\psi$ is a diffeomorphism.

In particular, $X$ and $Y$ are diffemorphic.


Proof