Fukaya categories of symmetric products and bordered Heegaard-Floer homology

Details Fukaya categories of symmetric products and bordered Heegaard-Floer homology Fukaya categories of symmetric products and bordered Heegaard-Floer homology

2010-01-25

arxiv.org/abs/1001.4323v3

Mathematics

Geometric Topology

54 pages, 11 figures; v3: minor revisions, to appear in J Gokova Geometry Topology

Scientific paper

The main goal of this paper is to discuss a symplectic interpretation of Lipshitz, Ozsvath and Thurston's bordered Heegaard-Floer homology in terms of Fukaya categories of symmetric products and Lagrangian correspondences. More specifically, we give a description of the algebra A(F) which appears in the work of Lipshitz, Ozsvath and Thurston in terms of (partially wrapped) Floer homology for product Lagrangians in the symmetric product, and outline how bordered Heegaard-Floer homology itself can conjecturally be understood in this language.

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