TY - JOUR
T1 - On the naturality of the spectral sequence from khovanov homology to heegaard floer homology
AU - Grigsby, J. Elisenda
AU - Wehrli, Stephan M.
N1 - Funding Information:
We thank John Baldwin, Matt Hedden, Nathan Habegger, András Juhász, Mikhail Khovanov, Rob Kirby, Robert Lipshitz, Peter Ozsváth, Lawrence Roberts, and Liam Watson for interesting conversations. We are particularly indebted to Robert Lipshitz for providing us with both the key idea in the proof of Theorem 4.5 and extremely valuable feedback on a preliminary draft. A portion of this work was completed while the second author was a visiting postdoctoral fellow at Columbia University, supported by a Swiss National Science Foundation fellowship for prospective researchers. We are grateful to the Columbia mathematics department for its hospitality.
Funding Information:
J.E.G. was partially supported by a National Science Foundation (NSF) postdoctoral fellowship and NSF grant number DMS-0905848. S.W. was supported by a postdoctoral fellowship of the Fondation Sciences Mathématiques de Paris.
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
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U2 - 10.1093/imrn/rnq039
DO - 10.1093/imrn/rnq039
M3 - Article
AN - SCOPUS:78049524597
SN - 1073-7928
VL - 2010
SP - 4159
EP - 4210
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 21
ER -