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Tautological classes and symmetry in Khovanov-Rozansky homology Gorsky, Eugene


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. This is a joint work with Matt Hogancamp and Anton Mellit.

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