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Transactions of the American Mathematical Society

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Sutured Khovanov homology, Hochschild homology, and the Ozsváth-Szabó spectral sequence


Authors: Denis Auroux, J. Elisenda Grigsby and Stephan M. Wehrli
Journal: Trans. Amer. Math. Soc. 367 (2015), 7103-7131
MSC (2010): Primary 20F36, 57M27; Secondary 81R50, 57R58
DOI: https://doi.org/10.1090/S0002-9947-2015-06252-7
Published electronically: April 1, 2015
MathSciNet review: 3378825
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Abstract: In 2002, Khovanov-Seidel constructed a faithful action of the
$ (m+1)$-strand braid group, $ \mathfrak{B}_{m+1}$, on the derived category of left modules over a quiver algebra, $ A_m$. We interpret the Hochschild homology of the Khovanov-Seidel braid invariant as a direct summand of the sutured Khovanov homology of the annular braid closure.


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Additional Information

Denis Auroux
Affiliation: Department of Mathematics, 970 Evans Hall #3840, University of California Berkeley, Berkeley, California 94720
Email: auroux@math.berkeley.edu

J. Elisenda Grigsby
Affiliation: Department of Mathematics, 301 Carney Hall, Boston College, Chestnut Hill, Massachusetts 02467
Email: grigsbyj@bc.edu

Stephan M. Wehrli
Affiliation: Department of Mathematics, 215 Carnegie, Syracuse University, Syracuse, New York 13244
Email: smwehrli@syr.edu

DOI: https://doi.org/10.1090/S0002-9947-2015-06252-7
Received by editor(s): May 9, 2013
Received by editor(s) in revised form: July 26, 2013
Published electronically: April 1, 2015
Additional Notes: The first author was partially supported by NSF grant DMS-1007177.
The second author was partially supported by NSF grant DMS-0905848 and NSF CAREER award DMS-1151671.
The third author was partially supported by NSF grant DMS-1111680.
Article copyright: © Copyright 2015 American Mathematical Society

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