Sutured annular Khovanov-Rozansky homology
Quantum Algebra
2015-06-29 v1 Geometric Topology
Representation Theory
Abstract
We introduce an 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 sl(2) foams and categorified quantum gl(m), via classical skew Howe duality. This framework then extends to give our annular sl(n) link homology theory, which we call sutured annular Khovanov-Rozansky homology. We show that the sl(n) sutured annular Khovanov-Rozansky homology of an annular link carries an action of the Lie algebra sl(n), which in the n=2 case recovers a result of Grigsby-Licata-Wehrli.
Keywords
Cite
@article{arxiv.1506.08188,
title = {Sutured annular Khovanov-Rozansky homology},
author = {Hoel Queffelec and David E. V. Rose},
journal= {arXiv preprint arXiv:1506.08188},
year = {2015}
}
Comments
29 pages, many figures