Hamiltonian handleslides for Heegaard Floer homology

Timothy Perutz

Hamiltonian handleslides for Heegaard Floer homology

Symplectic Geometry 2008-02-27 v2 Geometric Topology

Authors: Timothy Perutz

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.

Keywords

Heegaard Floer homology Hamiltonian isotopy Lagrangian submanifolds handleslide symplectic forms Riemann surface symmetric product

Cite

@article{arxiv.0801.0564,
  title  = {Hamiltonian handleslides for Heegaard Floer homology},
  author = {Timothy Perutz},
  journal= {arXiv preprint arXiv:0801.0564},
  year   = {2008}
}

Comments

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

Hamiltonian handleslides for Heegaard Floer homology

Abstract

Keywords

Cite

Comments

Related papers