Tautological classes and symmetry in Khovanov-Rozansky homology

2021/03/01 by Eugene Gorsky, Gorsky, Eugene, Matthew Hogancamp +3 · 4 citations
Mathematics · #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2103.01212

openalex publication_date 2021/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 F₂ satisfies ``hard Lefshetz property" and hence exhibits the symmetry in Khovanov-Rozansky homology conjectured by Dunfield, Gukov and Rasmussen.

Citations

• Khovanov-Rozansky homology and higher Catalan sequences
• Dualizable link homology

Cited by

• Doubly-graded exponential growth of colored torus knot homology
• A local \mathfrakgl_1|1-action on odd Khovanov homology
• Stable deformed \mathfrakgl_N homology of torus knots
• Computations of HOMFLY homology

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