 
Summary: Proceedings of the International Congress of Mathematicians
Hyderabad, India, 2010
Fukaya categories and bordered Heegaard
Floer homology
Denis Auroux
Abstract. We outline an interpretation of HeegaardFloer homology of 3manifolds
(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 prod
uct and the bordered algebra introduced by Robert Lipshitz, Peter Ozsv´ath and Dylan
Thurston, and recast bordered HeegaardFloer homology in this language.
Mathematics Subject Classification (2000). 53D40 (57M27, 57R58)
Keywords. Bordered HeegaardFloer homology, Fukaya categories
1. Introduction
In its simplest incarnation, HeegaardFloer homology associates to a closed 3
manifold Y a graded abelian group HF(Y ). This invariant is constructed by
considering a Heegaard splitting Y = Y1 Y2 of Y into two genus g handlebodies,
each of which determines a product torus in the gfold symmetric product of the
Heegaard surface = Y1 = Y2. Deleting a marked point z from to obtain
an open surface, HF(Y ) is then defined as the Lagrangian Floer homology of the
