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

TL;DR

This paper constructs exotic smooth structures on ^4 with large, nontrivial compactly supported diffeomorphism groups, advancing understanding of smooth topology in four dimensions.

Contribution

It introduces a new method to create exotic ^4 with arbitrarily large rank of compactly supported diffeomorphisms, modifying previous cork constructions.

Findings

Exotic ^4 with nontrivial mapping class groups

Construction of examples with arbitrarily large rank

Modification of cork exteriors to be simply-connected

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.