Tautological classes and symmetry in Khovanov-Rozansky homology

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.

64 pages, accepted in Duke Math. J

References in corpus (4)

• Cell decompositions of character varieties
• Torus link homology
• Soergel bimodules and matrix factorizations
• Diagonals and A-infinity Tensor Products

Cited by in corpus (1)

• Algebra and geometry of link homology