Fray functors and equivalence of colored HOMFLYPT homologies
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908532259946496 |
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| author | Conners, Luke |
| author_facet | Conners, Luke |
| contents | We construct several families of functors on the homotopy category of singular Soergel bimodules that mimic cabling and insertion of column-colored projectors. We use these functors to identify the intrinsically-colored homology of Webster--Williamson and the projector-colored homology of Elias--Hogancamp for an arbitrary link, up to multiplication by a polynomial in the quantum degree $q$. Combined with the results of arXiv:2303.16271, this establishes parity results for the intrinsic column-colored homology of positive torus knots, partially resolving a conjecture of Hogancamp--Rose--Wedrich in arXiv:2107.09590. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00875 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fray functors and equivalence of colored HOMFLYPT homologies Conners, Luke Quantum Algebra Geometric Topology We construct several families of functors on the homotopy category of singular Soergel bimodules that mimic cabling and insertion of column-colored projectors. We use these functors to identify the intrinsically-colored homology of Webster--Williamson and the projector-colored homology of Elias--Hogancamp for an arbitrary link, up to multiplication by a polynomial in the quantum degree $q$. Combined with the results of arXiv:2303.16271, this establishes parity results for the intrinsic column-colored homology of positive torus knots, partially resolving a conjecture of Hogancamp--Rose--Wedrich in arXiv:2107.09590. |
| title | Fray functors and equivalence of colored HOMFLYPT homologies |
| topic | Quantum Algebra Geometric Topology |
| url | https://arxiv.org/abs/2405.00875 |