Exotic ${\mathbb{R}}^4$'s with Compactly Supported Diffeomorphisms

Abstract

We construct exotic copies of ${\mathbb{R}}^4$ with nontrivial compactly supported mapping class groups of arbitrarily large rank. This follows from a modification of the construction of the diffeomorphism corks of arXiv:2407.04696 that makes their exteriors simply-connected.