Khovanov-Rozansky homology and 2-braid groups
Representation Theory
2012-03-23 v1
Abstract
Khovanov has given a construction of the Khovanov-Rozansky link invariants (categorifying the HOMFLYPT invariant) using Hochschild cohomology of 2-braid groups. We give a direct proof that his construction does give link invariants. We show more generally that, for any finite Coxeter group, his construction provides a Markov "2-trace", and we actually show that the invariant takes value in suitable derived categories. This makes more precise a result of Trafim Lasy who has shown that, after taking the class in K_0, this provides a Markov trace.
Keywords
Cite
@article{arxiv.1203.5065,
title = {Khovanov-Rozansky homology and 2-braid groups},
author = {Raphaël Rouquier},
journal= {arXiv preprint arXiv:1203.5065},
year = {2012}
}