A short note on $\ddot{I}{€}_1{\mathrm{Diff}}_{\partial }(D^{4k})$ for $k\ge 3$

Abstract

Let ${\mathrm{Diff}}_{\partial }(D^n)$ be the topological group of diffeomorphisms of $D^n$ which agree with the identity near the boundary. In this short note, we compute the fundamental groups $\ddot{I}{€}_1{\mathrm{Diff}}_{\partial }(D^{4k})$ for $k\ge 3$.

7 Pages. Some improvements and corrections based on two anonymous referees' reports. Final version, to appear in Proc. AMS