A cylindrical reformulation of Heegaard Floer homology
Abstract
We reformulate Heegaard Floer homology in terms of holomorphic curves in the cylindrical manifold Sigma x [0,1] x R, where Sigma is the Heegaard surface, instead of Sym^g(Sigma). We then show that the entire invariance proof can be carried out in our setting. In the process, we derive a new formula for the index of the dbar-operator in Heegaard Floer homology, and shorten several proofs. After proving invariance, we show that our construction is equivalent to the original construction of Ozsvath-Szabo. We conclude with a discussion of elaborations of Heegaard Floer homology suggested by our construction, as well as a brief discussion of the relation with a program of C Taubes.
Keywords
Cite
@article{arxiv.math/0502404,
title = {A cylindrical reformulation of Heegaard Floer homology},
author = {Robert Lipshitz},
journal= {arXiv preprint arXiv:math/0502404},
year = {2009}
}
Comments
This is the version published by Geometry & Topology on 9 August 2006