On the naturality of the spectral sequence from Khovanov homology to Heegaard Floer homology

J. Elisenda Grigsby; Stephan M. Wehrli

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arXiv · 0907.4378

On the naturality of the spectral sequence from Khovanov homology to Heegaard Floer homology

J. Elisenda Grigsby·Stephan M. Wehrli

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Abstract

Ozsvath and Szabo have established an algebraic relationship, in the form of a spectral sequence, between the reduced Khovanov homology of (the mirror of) a link L in S^3 and the Heegaard Floer homology of its double-branched cover. This relationship has since been recast by the authors 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 Juhasz. In the present work we prove the naturality of the spectral sequence under certain elementary TQFT operations, using a generalization of Juhasz's surface decomposition theorem valid for decomposing surfaces geometrically disjoint from an imbedded framed link.

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BibTeX RIS

J. Elisenda Grigsby, Stephan M. Wehrli. 2009-07-27. On the naturality of the spectral sequence from Khovanov homology to Heegaard Floer homology. https://arxiv.org/abs/0907.4378

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