Exotic Four-Manifolds, Corks, and Heegaard Floer Homology

Akbulut corks provide a topological avenue for understanding the smooth structures of a closed four-manifold. Computing the Heegaard Floer invariants is a first step towards understanding them. To this end, the Heegaard Floer homology of the bounding three-manifolds of the Mazur corks is computed.