Let L ⊂ S3 be a link. We study the Heegaard Floer homology of the branched double-cover ∑(L) of S3, branched along L. When L is an alternating link, HF 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 E2 term is a suitable variant of Khovanov's homology for the link L, converging to the Heegaard Floer homology of ∑(L).
All Science Journal Classification (ASJC) codes
- Alternating links
- Branched double-covers
- Heegaard Floer homology
- Khovanov's homology