# Question concerning h-cobordisms

Suppose we have a cobordism $W$ of manifolds $M_0$ and $M_1$ and suppose the inclusion of $M_0$ into $W$ is a homotopy equivalence. Is the same true for the inclusion of $M_1$ (ie. is $W$ already an h-cobordism)?

Using Poincare Lefschetz duality one can show that this map induces isomorphisms on homology. Hence it suffices to show that the inclusion $M_1\rightarrow W$ induces an isomorphism on $\pi_1$.

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However, the answer is "yes" after stabilizing three times: The product $W \times J^3$ (where $J^3$ is a $3$-cube) is an $h$-cobordism from $M_0 \times J^3$ to the closure of the remaining part of the boundary. There are details in Remark 1.1.3 of my book project "Spaces of PL manifolds and categories of simple maps" with Jahren and Waldhausen.