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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Sutured annular Khovanov-Rozansky homology
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by Hoel Queffelec and David E. V. Rose PDF
Trans. Amer. Math. Soc. 370 (2018), 1285-1319 Request permission

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
  • MR Author ID: 1104235
  • 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
  • MR Author ID: 830033
  • Email: davidrose@unc.edu
  • 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
  • © Copyright 2017 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 370 (2018), 1285-1319
  • MSC (2010): Primary 17B37, 57M25, 57M27, 81R50
  • DOI: https://doi.org/10.1090/tran/7117
  • MathSciNet review: 3729501