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On the Heegaard Floer homology of branched double-covers
Authors:Peter Ozsváth  Zoltán Szabó
Institution:a Department of Mathematics, Columbia University, NY 10027, USA
b Department of Mathematics, Princeton University, Princeton, NJ 08540, USA
Abstract:Let View the MathML source 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, View the MathML source 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).
Keywords:Heegaard Floer homology  Branched double-covers  Khovanov's homology  Alternating links
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