Knot Floer homology and integer surgeries

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Abstract

Let Y be a closed three manifold with trivial first homology, and let K⊂Y be a knot. We give a description of the Heegaard Floer homology of integer surgeries on Y along K in terms of the filtered homotopy type of the knot invariant for K. As an illustration of these techniques, we calculate the Heegaard Floer homology groups of non trivial circle bundles over Riemann surfaces (with coefficients in Z/2Z).

Original languageEnglish (US)
Pages (from-to)101-153
Number of pages53
JournalAlgebraic and Geometric Topology
Volume8
Issue number1
DOIs
StatePublished - 2008

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Keywords

  • Knot floer homology
  • Surgery theory

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