Fukaya categories and bordered Heegaard-Floer homology

摘要

We outline an interpretation of Heegaard-Floer homology of 3-manifolds(closed or with boundary) in terms of the symplectic topology of symmetricproducts of Riemann surfaces, as suggested by recent work of Tim Perutz andYanki Lekili. In particular we discuss the connection between the Fukayacategory of the symmetric product and the bordered algebra introduced by RobertLipshitz, Peter Ozsvath and Dylan Thurston, and recast bordered Heegaard-Floerhomology in this language.