# Heegaard Floer Homology and Closed Exotic 4-Manifolds

## Location

We discuss new methods for using the Heegaard Floer homology

of hypersurfaces to distinguish between smooth closed 4-manifolds that

are homeomorphic but non-diffeomorphic. Specifically, for a 4-manifold X

with b_1(X)=1, the minimum rank of the reduced Heegaard Floer homology

of any embedded 3-manifold X representing a generator of H_1(X) gives a

diffeomorphism invariant of X. We use this invariant to distinguish

certain infinite families of exotic 4-manifolds that cannot be

distinguished by previously known techniques. Using related ideas, we

also provide the first known examples of (non-simply-connected) exotic

4-manifolds with negative definite intersection form. This is joint work

with Tye Lidman and Lisa Piccirillo.