On the naturality of the spectral sequence from khovanov homology to heegaard floer homology

J. Elisenda Grigsby, Stephan M. Wehrli

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2 Scopus citations

Abstract

In [18], Ozsváth-Szabó established an algebraic relationship, in the form of a spectral sequence, between the reduced Khovanov homology of (the mirror of) a link and the Heegaard Floer homology of its double-branched cover. This relationship, extended in [19] and [4], was recast, in [5], as a specific instance of a broader connection between Khovanov- and Heegaard Floer-type homology theories, using a version of Heegaard Floer homology for sutured manifolds developed by Juhász in [7]. In the present work, we prove the naturality of the spectral sequence under certain elementary operations, using a generalization of Juhász's surface decomposition theorem valid for decomposing surfaces geometrically disjoint from an imbedded framed link.

Original languageEnglish (US)
Pages (from-to)4159-4210
Number of pages52
JournalInternational Mathematics Research Notices
Volume2010
Issue number21
DOIs
StatePublished - 2010

ASJC Scopus subject areas

  • Mathematics(all)

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