Sutured annular Khovanov-Rozansky homology

• Published in: Transactions of the American Mathematical Society Vol. 370; no. 2; pp. 1285 - 1319
• Main Authors: QUEFFELEC, HOEL, ROSE, D DAVID E. V.
• Format: Journal Article
• Language: English
• Published: American Mathematical Society 01-02-2018
• Subjects: Mathematics; Quantum Algebra
• ISSN: 0002-9947; 1088-6850
• DOI: 10.1090/tran/7117

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.