On the Heegaard Floer homology of branched double-covers

  title={On the Heegaard Floer homology of branched double-covers},
  author={Peter S. Ozsvath and Zolt{\'a}n Imre Szab{\'o}},
  journal={Advances in Mathematics},
Abstract Let L ⊂ S 3 be a link. We study the Heegaard Floer homology of the branched double-cover Σ ( L ) of S 3 , 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 E 2 term is a suitable variant of Khovanov's homology for the link L, converging to the Heegaard Floer homology of Σ ( L ) . 
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