Equivariant Corks

TL;DR

This paper constructs specific contractible 4-manifolds with finite group actions on their boundaries, enabling the generation of multiple distinct smooth structures through boundary regluing, advancing understanding of 4-manifold topology.

Contribution

It introduces a method to produce contractible 4-manifolds with boundary actions that produce different smoothings via group-based boundary modifications.

Findings

Constructed contractible 4-manifolds with finite group actions.

Demonstrated how boundary regluing yields distinct smooth 4-manifolds.

Provided new examples of exotic smooth structures in 4-manifold topology.

Abstract

For suitable finite groups G, we construct contractible 4-manifolds C with an effective G-action on $\partial C$ whose associated pairs (C,g) for all $g \in G$ are distinct smoothings of the pair $(C,\partial C)$. Indeed C embeds in a 4-manifold so that cutting out C and regluing using distinct elements of G yield distinct smooth 4-manifolds.