Tautological classes for (n,n+1) torus knots

Eugene Gorsky; Anton Mellit

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arXiv · 2601.16877

Tautological classes for (n,n+1) torus knots

Eugene Gorsky·Anton Mellit

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Abstract

We construct an explicit isomorphism between the HOMFLY-PT homology of $(n,n+1)$ torus knots and the direct sum of hook isotypic components of the space of diagonal coinvariants. As a consequence, we compute the action of tautological classes in HOMFLY-PT homology of $(n,n+1)$ torus knots and prove that it extends to an action of the Lie algebra of Hamiltonian vector fields on the plane. We also compute the action of differentials $d_N$ in Rasmussen spectral sequences from HOMLFY-PT to $\mathfrak{gl}(N)$ homology of $(n,n+1)$ torus knots.

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BibTeX RIS

Eugene Gorsky, Anton Mellit. 2026-01-23. Tautological classes for (n,n+1) torus knots. https://arxiv.org/abs/2601.16877

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