Bordered Floer homology and the branched double cover I

Details Bordered Floer homology and the branched double cover I Bordered Floer homology and the branched double cover I

2010-11-02

arxiv.org/abs/1011.0499v1

Mathematics

Geometric Topology

43 pages, 16 figures

Scientific paper

Given a link in the three-sphere, Z. Szab\'o and the second author constructed a spectral sequence starting at the Khovanov homology of the link and converging to the Heegaard Floer homology of its branched double-cover. The aim of this paper and its sequel is to explicitly calculate this spectral sequence, using bordered Floer homology. There are two primary ingredients in this computation: an explicit calculation of filtered bimodules associated to Dehn twists and a pairing theorem for polygons. In this paper we give the first ingredient, and so obtain a combinatorial spectral sequence from Khovanov homology to Heegaard Floer homology; in the sequel we show that this spectral sequence agrees with the previously known one.

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