Sutured annular Khovanov-Rozansky homology

Queffelec, Hoel; Rose, David

doi:10.1090/tran/7117

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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