On the spectral sequence from Khovanov homology to Heegaard Floer homology

Details On the spectral sequence from Khovanov homology to Heegaard Floer homology On the spectral sequence from Khovanov homology to Heegaard Floer homology

2008-09-19

arxiv.org/abs/0809.3293v4

Mathematics

Geometric Topology

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

Scientific paper

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).

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