Bordered Floer homology and the spectral sequence of a branched double cover I

Robert Lipshitz; Peter S. Ozsváth; Dylan P. Thurston

doi:10.1112/jtopol/jtu012

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arXiv · 1011.0499

Bordered Floer homology and the spectral sequence of a branched double cover I

Robert Lipshitz·Peter S. Ozsváth·Dylan P. Thurston

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Abstract

Given a link in the three-sphere, Z. Szabó 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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Robert Lipshitz, Peter S. Ozsváth, Dylan P. Thurston. 2016-01-11. Bordered Floer homology and the spectral sequence of a branched double cover I. https://doi.org/10.1112/jtopol%2Fjtu012

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