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Tautological classes and symmetry in Khovanov-Rozansky homology

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arxiv 2103.01212 v2 pith:HOUWQRWR submitted 2021-03-01 math.RT math.GTmath.QA

Eugene Gorsky , Matthew Hogancamp , Anton Mellit This is my paper · ORCID
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keywords homologykhovanov-rozanskyclassessymmetrytautologicalactioncharactercohomology
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abstract

We define a new family of commuting operators $F_k$ in Khovanov-Rozansky link homology, similar to the action of tautological classes in cohomology of character varieties. We prove that $F_2$ satisfies ``hard Lefshetz property" and hence exhibits the symmetry in Khovanov-Rozansky homology conjectured by Dunfield, Gukov and Rasmussen.

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  1. Remarks on some infinitesimal symmetries of Khovanov--Rozansky homologies in finite characteristic

    math.GT 2024-12 conditional novelty 6.0 of 10

    A p-differential algebra argument reproves base point independence for characteristic-p Khovanov-Rozansky homology and yields new sl2-symmetry consequences for link homology.

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