### Heegaard Floer Homology and Closed Exotic 4-Manifolds

- Series
- Geometry Topology Seminar
- Time
- Monday, January 29, 2024 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Adam Levine – Duke

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.