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Tautological classes and symmetry in Khovanov-Rozansky homology
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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.
Forward citations
Cited by 2 Pith papers
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Global Weyl modules for thin Lie algebras are finite-dimensional
A new class of Lie algebras, called thin Lie algebras, is shown to have finite-dimensional global Weyl modules, with the Hamiltonian vector fields on the plane as the motivating example.
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Remarks on some infinitesimal symmetries of Khovanov--Rozansky homologies in finite characteristic
A p-differential algebra argument reproves base point independence for characteristic-p Khovanov-Rozansky homology and yields new sl2-symmetry consequences for link homology.
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