Event Series
Event Type
Tuesday, May 16, 2023 4:00 PM
Adam Levine (Duke University)

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.