On the Heegaard Floer homology of branched double-covers

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Abstract

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).

Original languageEnglish (US)
Pages (from-to)1-33
Number of pages33
JournalAdvances in Mathematics
Volume194
Issue number1
DOIs
StatePublished - Jun 20 2005

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Alternating links
  • Branched double-covers
  • Heegaard Floer homology
  • Khovanov's homology

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