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# Adam Levine : Heegaard Floer Homology and Closed Exotic 4-Manifolds

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.

**Category**: Geometry and Topology**Duration**: 01:04:30**Date**: September 11, 2023 at 3:10 PM**Views**: 75-
**Tags:**seminar, Geometry and Topology Seminar

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