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Sutured annular Khovanov-Rozansky homology


Authors: Hoel Queffelec and David E. V. Rose
Journal: Trans. Amer. Math. Soc. 370 (2018), 1285-1319
MSC (2010): Primary 17B37, 57M25, 57M27, 81R50
DOI: https://doi.org/10.1090/tran/7117
Published electronically: October 5, 2017
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Abstract: We introduce an $ \mathfrak{sl}_n$ homology theory for knots and links in the thickened annulus. To do so, we first give a fresh perspective on sutured annular Khovanov homology, showing that its definition follows naturally from trace decategorifications of enhanced $ \mathfrak{sl}_{2}$ foams and categorified quantum $ \mathfrak{gl}_m$, via classical skew Howe duality. This framework then extends to give our annular $ \mathfrak{sl}_n$ link homology theory, which we call sutured annular Khovanov-Rozansky homology. We show that the $ \mathfrak{sl}_n$ sutured annular Khovanov-Rozansky homology of an annular link carries an action of the Lie algebra $ \mathfrak{sl}_n$, which in the $ n=2$ case recovers a result of Grigsby-Licata-Wehrli.


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Additional Information

Hoel Queffelec
Affiliation: CNRS and Institut Montpelliérain Alexander Grothendieck, Université de Montpellier, 34095 Montpellier Cedex 5, France
Email: hoel.queffelec@umontpellier.fr

David E. V. Rose
Affiliation: Department of Mathematics, University of North Carolina, Phillips Hall CB #3250, UNC-CH, Chapel Hill, North Carolina 27599-3250
Email: davidrose@unc.edu

DOI: https://doi.org/10.1090/tran/7117
Received by editor(s): July 23, 2015
Received by editor(s) in revised form: June 28, 2016
Published electronically: October 5, 2017
Additional Notes: The first author was funded by the ARC DP 140103821
The second author was partially supported by the John Templeton Foundation and NSF grant DMS-1255334
Article copyright: © Copyright 2017 American Mathematical Society

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