English

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}
}
R2 v1 2026-06-21T20:38:33.208Z