On the spectral sequence from Khovanov homology to Heegaard Floer homology

By John A. Baldwin. 2008

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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).

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/52b9bba6bb92fd3b168db62704fb84b5d9c075bc

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Citations in the corpus

A link surgery spectral sequence in monopole Floer homology (2009, background): “In [2], Baldwin defines such a map φ for each of the three Reidemeister moves.”
Khovanov homology is an unknot-detector (2010, background): “More generally, one can ask whether the intermediate pages of the spectral sequence, as filtered groups, are invariants of K (see [2] for the similar question concerning the spectral sequence of Ozsváth and Szabó).”
Khovanov module and the detection of unlinks (2012, background): “Their result had numerous antecedents [1, 2, 3, 10, 11, 12, 13, 37], most aimed at generalizing or exploiting a spectral sequence discovered by Ozsváth and Szabó [31] which begins at Khovanov homology and converges to the Heegaard Floer homology of the branched double cover.”