On the Heegaard Floer homology of branched double-covers

Abstract

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 $\Sigma (L)$.

36 pages, 12 figures

Cited by in corpus (2)

• Monopoles and lens space surgeries
• Knots with unknotting number one and Heegaard Floer homology