On the homotopy type of \(Diff(\Sigma ^ n)\)
In this note it is shown that, for each prime p there is an exotic sphere \(\Sigma ^ n\) with \[ \pi _ i(Diff(\Sigma ^ n)) \otimes {\mathbb{Z}}[1/p]\simeq \pi _ i(Diff(S^ n)) \otimes {\mathbb{Z}}[1/p] \] for all i but with \(\pi _ j(Diff(\Sigma ^ n))\not\simeq \pi _ j(Diff(S^ n))\) for some j.
homotopy groups of groups of diffeomorphisms
scientific article; zbMATH DE number 3971788