Fukaya categories of symmetric products and bordered Heegaard-Floer homology

• Main Author: Auroux, Denis (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
• Format: Article
• Language: English
• Published: Scientific and Technical Research Council of Turkey, 2011-03-04T14:56:30Z.
• Subjects: Article
• Online Access: Get fulltext

http://gokovagt.org/journal/2010/auroux.html
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.
National Science Foundation (U.S.) (DMS-0600148)
National Science Foundation (U.S.) (DMS-0652630)