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Khovanov-Rozansky homology and 2-braid groups

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arxiv 1203.5065 v1 pith:7TXPSI5T submitted 2012-03-22 math.RT

Raphaël Rouquier This is my paper · ORCID
classification math.RT
keywords constructionbraidgivegroupsinvariantinvariantskhovanov-rozanskylink
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Instanton slices and their superpolynomials

    math.AG 2026-07 conditional novelty 7.0 of 10

    Motivic superpolynomials of plane-curve singularities are repackaged as "instanton slice" counts, conjecturally matching new DAHA superpolynomials that are claimed to produce superpolynomials for hyperbolic knots.

  2. HOMFLYPT homology for links in handlebodies via type A Soergel bimodules

    math.QA 2019-08 accept novelty 7.0 of 10

    Links in genus-g handlebodies are assigned a triply-graded homology built from singular Soergel bimodules and Hochschild cohomology, generalizing colored HOMFLYPT homology.

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