Session S10 - Categorification, Higher Representation Theory, and Homological Knot Invariants

Tuesday, July 20, 16:45 ~ 17:20 UTC-3

Tautological classes and symmetry in Khovanov-Rozansky homology

Eugene Gorsky

University of California, Davis, United States   -   egorskiy@math.ucdavis.edu

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.

Joint work with Matt Hogancamp (Northeastern University, USA) and Anton Mellit (University of Vienna, Austria).

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