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Jonathan Hanselman, RLM 12.166: Heegaard Floer invariants for manifolds with torus boundary
Monday, October 15, 2018, 02:00pm - 03:00pm
To a 3-manifold with torus boundary, we can associate an elementof the Fukaya category of the punctured torus--that is, a collectionof immersed curves in the torus, decorated with local systems--suchthat when two such manifolds are glued the Heegaard Floer homologyof resulting 3-manifold is recovered from Floer homology of thecorresponding curves. These curves are a reformulation of thebordered Heegaard Floer defined by Lipshitz, Ozsvath, and Thurston,but their geometric nature makes them more user friendly. Wewill discuss some properties of these curves and some applications,including invariance of Heegaard Floer homology under genus onemutation and a rank inequality for Heegaard Floer homology oftoroidal manifolds. This is joint work with J. Rasmussen andL. Watson.
Location: RLM 12.166

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