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 symmetric products of Riemann surfaces, as suggested by recent work of Tim Perutz and Yanki Lekili. In particular we discuss the connection between the Fukaya category of the symmetric product and the bordered algebra introduced by Robert Lipshitz, Peter Ozsvath and Dylan Thurston, and recast bordered Heegaard-Floer homology in this language.