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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.00175 |
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| _version_ | 1866912458828939264 |
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| author | Ballinger, William Gorsky, Eugene Hogancamp, Matthew Wang, Joshua |
| author_facet | Ballinger, William Gorsky, Eugene Hogancamp, Matthew Wang, Joshua |
| contents | We compute the $E_2$ page in the Rasmussen spectral sequence from triply graded to $\mathfrak{gl}_N$ Khovanov--Rozansky stable homology of torus knots. This confirms a weak form of the conjecture of the second author, Oblomkov, and Rasmussen. The main tool is the link-splitting deformation, or $y$-ification, of link homology; in the $y$-ified context, the relevant Rasmussen spectral sequence collapses and we explicitly compute the $y$-ified $\mathfrak{gl}_N$ stable Khovanov--Rozansky homology of torus knots for all $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00175 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stable deformed $\mathfrak{gl}_N$ homology of torus knots Ballinger, William Gorsky, Eugene Hogancamp, Matthew Wang, Joshua Geometric Topology 57K18 We compute the $E_2$ page in the Rasmussen spectral sequence from triply graded to $\mathfrak{gl}_N$ Khovanov--Rozansky stable homology of torus knots. This confirms a weak form of the conjecture of the second author, Oblomkov, and Rasmussen. The main tool is the link-splitting deformation, or $y$-ification, of link homology; in the $y$-ified context, the relevant Rasmussen spectral sequence collapses and we explicitly compute the $y$-ified $\mathfrak{gl}_N$ stable Khovanov--Rozansky homology of torus knots for all $N$. |
| title | Stable deformed $\mathfrak{gl}_N$ homology of torus knots |
| topic | Geometric Topology 57K18 |
| url | https://arxiv.org/abs/2507.00175 |