Equivariant corks

Abstract

For any finite subgroup G of SO(4), we construct a contractible 4-manifold C with a 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. If we simply require G to be a subgroup of the mapping class group of the boundary, then such examples exist for groups that cannot act on any homology sphere.