Equivariant corks

Abstract

For any finite subgroup $G$ of $SO\left(4\right)$, we construct a contractible $4$–manifold $C$, with an effective $G$–action on its boundary, that can be embedded in a closed $4$–manifold so that cutting $C$ out and regluing using distinct elements of $G$ will always yield distinct smooth $4$–manifolds.