On the functoriality of the space of equivariant smooth $h$-cobordisms

Thomas Goodwillie, Kiyoshi Igusa, Cary Malkiewich +1

We construct an $(\infty ,1)$-functor that takes each smooth $G$-manifold with corners $M$ to the space of equivariant smooth $h$-cobordisms ${\mathcal{H}}_{\mathrm{Diff}}(M)$. We al…