Fukaya categories of symmetric products and bordered Heegaard-Floer homology
Denis Auroux
TL;DR
This paper explores a symplectic geometric interpretation of bordered Heegaard-Floer homology using Fukaya categories of symmetric products and Lagrangian correspondences, providing a new conceptual framework.
Contribution
It offers a description of the algebra A(F) in bordered Heegaard-Floer homology via Floer homology of product Lagrangians, linking it to symplectic geometry.
Findings
Description of algebra A(F) through Floer homology
Outline of a conjectural symplectic interpretation of bordered Heegaard-Floer homology
Connection between Lagrangian correspondences and algebraic structures in Floer theory
Abstract
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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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models