On the Heegaard Floer homology of branched double-covers

Details On the Heegaard Floer homology of branched double-covers On the Heegaard Floer homology of branched double-covers

2003-09-09

arxiv.org/abs/math/0309170v1

Adv. Math. 194 (2005), no. 1, 1--33.

Mathematics

Geometric Topology

36 pages, 12 figures

Scientific paper

Let $L\subset S^3$ be a link. We study the Heegaard Floer homology of the branched double-cover $\Sigma(L)$ of $S^3$, branched along $L$. When $L$ is an alternating link, $\HFa$ of its branched double-cover has a particularly simple form, determined entirely by the determinant of the link. For the general case, we derive a spectral sequence whose $E^2$ term is a suitable variant of Khovanov's homology for the link $L$, converging to the Heegaard Floer homology of $\Sigma(L)$.

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