Seminar

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Heegaard-Floer homology was originally introduced by Ozsvath-Szabo as a variation of Lagrangian-Floer homology of a space associated to a Heegaard diagram. It was then generalized to compact three manifolds with boundary, where we associated to the boundary a strand algebra, the three manifold with boundary a module over the strand algebra, and they should glue to our Heegaard-Floer homology. Auroux showed that the strand algebras associated to the bordered Floer homology, or more generally some algebras coming from an open Riemann surface, generate the Fukaya category of the space. In this talk I’ll introduce the construction of Heegaard-Floer, bordered Floer and Ozsvath-Szabo algebras, Fukaya category of the symmetric product of Riemann surfaces, and Auroux’ work on generation results. It’s a special case of my joint work in progress with Sukjoo Lee, Yin Li and Cheuk-Yu Mak.