Tautological classes for (n,n+1) torus knots
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912843899600896 |
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| author | Gorsky, Eugene Mellit, Anton |
| author_facet | Gorsky, Eugene Mellit, Anton |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16877 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tautological classes for (n,n+1) torus knots Gorsky, Eugene Mellit, Anton Geometric Topology Combinatorics Representation Theory 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. |
| title | Tautological classes for (n,n+1) torus knots |
| topic | Geometric Topology Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2601.16877 |