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Gorsky, Eugene; Hogancamp, Matthew; Mellit, Anton

Tautological classes and symmetry in Khovanov-Rozansky homology. (English) Zbl 07928017

Duke Math. J. 173, No. 13, 2481-2561 (2024).
Summary: We define a new family of commuting operators \(F_k\) in Khovanov-Rozansky link homology, similar to the action of tautological classes in the 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.

MSC:

18N25 Categorification
20J05 Homological methods in group theory
57K18 Homology theories in knot theory (Khovanov, Heegaard-Floer, etc.)

Keywords:

DG algebra; Khovanov-Rozansky homology; Soergel bimodules; Khovanov-Rozansky homology
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References:

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