Infinite nonabelian corks

Abstract

We construct $G$-corks for any extension $G$ of ${\mathbb{Z}}^m$ by any finite subgroup of $\mathrm{SO}(4)$ and weakly equivariant $G$-corks for any extension $G$ of ${\mathbb{Z}}^m$ by any finite solvable group. In particular, this is the first example of $G$-corks for an infinite nonabelian group $G$ and answers a question by Tange. The construction is a combination of previous results by Auckly-Kim-Melvin-Ruberman, Gompf, and Tange. Using Gompf's results about exotic ${\mathbb{R}}^4$'s, we give an application to construct exotic ${\mathbb{R}}^4$'s whose diffeotopy group contains all poly-cyclic groups.

12 pages, 5 figures

References in corpus (2)

• Corks, Plugs and exotic structures
• Stable isotopy in four dimensions