On the Heegaard Floer homology of branched double-covers

Let L⊂S3 be a link. We study the Heegaard Floer homology of the branched double-cover Σ(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 Σ(L).