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Proceedings of the International Congress of Mathematicians Hyderabad, India, 2010

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 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 prod-
uct and the bordered algebra introduced by Robert Lipshitz, Peter Ozsv´ath and Dylan
Thurston, and recast bordered Heegaard-Floer homology in this language.
Mathematics Subject Classification (2000). 53D40 (57M27, 57R58)
Keywords. Bordered Heegaard-Floer homology, Fukaya categories
1. Introduction
In its simplest incarnation, Heegaard-Floer 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 g-fold 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


Source: Auroux, Denis - Department of Mathematics, Massachusetts Institute of Technology (MIT)


Collections: Mathematics