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

Author(s): Lipshitz, Robert; Ozsvath, Peter Steven; Thurston, Dylan P.

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Abstract: Given a link in the three-sphere, Z. Szabo 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.
Publication Date: Dec-2014
Electronic Publication Date: 30-Jul-2014
Citation: Lipshitz, Robert, Ozsvath, Peter S, Thurston, Dylan P. (2014). Bordered Floer homology and the spectral sequence of a branched double cover I. JOURNAL OF TOPOLOGY, 7 (1155 - 1199. doi:10.1112/jtopol/jtu012
DOI: doi:10.1112/jtopol/jtu012
ISSN: 1753-8416
EISSN: 1753-8424
Pages: 1155 - 1199
Type of Material: Journal Article
Journal/Proceeding Title: JOURNAL OF TOPOLOGY
Version: Author's manuscript

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