On the spectral sequence from Khovanov homology to Heegaard Floer homology

Abstract

Ozsvath and Szabo show that there is a spectral sequence whose E^2 term is the reduced Khovanov homology of L, and which converges to the Heegaard Floer homology of the (orientation reversed) branched double cover of S^3 along L. We prove that the E^k term of this spectral sequence is an invariant of the link L for all k >= 2. If L is a transverse link in the standard tight contact structure on S^3, then we show that Plamenevskaya's transverse invariant psi(L) gives rise to a transverse invariant, psi^k(L), in the E^k term for each k >= 2. We use this fact to compute each term in the spectral sequences associated to the torus knots T(3,4) and T(3,5).

Added 2 sections of background and section on independence of analytic data

References in corpus (6)

• Floer homology and knot complements
• A spanning tree model for the Heegaard Floer homology of a branched double-cover
• An algorithm for computing some Heegaard Floer homologies
• Notes on the Heegaard-Floer Link Surgery Spectral Sequence
• A link surgery spectral sequence in monopole Floer homology
• Khovanov homology, open books, and tight contact structures

Cited by in corpus (8)

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• A link surgery spectral sequence in monopole Floer homology
• Odd Khovanov homology is mutation invariant
• Computations of Szabó's Geometric Spectral Sequence in Khovanov Homology
• On the naturality of the spectral sequence from Khovanov homology to Heegaard Floer homology