Hamiltonian handleslides for Heegaard Floer homology

Abstract

A $g$-tuple of disjoint, linearly independent circles in a Riemann surface of genus $g$ determines a `Heegaard torus' in its $g$-fold symmetric product. Changing the circles by a handleslide produces a new torus. It is proved that, for symplectic forms with certain properties, these two tori are Hamiltonian-isotopic Lagrangian submanifolds. This provides an alternative route to the handleslide-invariance of Ozsvath-Szabo's Heegaard Floer homology.

24 pages, 2 figure. To appear in Proceedings of the 14th Gokova Geometry-Topology Conference. V2 has more detailed explanation of application to Heegaard Floer homology

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