Computing colored Khovanov homology
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918300380823552 |
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| author | von Merkl, Karim Ritter |
| author_facet | von Merkl, Karim Ritter |
| contents | We compare eight versions of finite-dimensional categorifications of the colored Jones polynomial and show that they yield isomorphic results over a field of characteristic zero. As an application, we verify a physics-motivated conjectural formula for colored superpolynomials based on Poincaré polynomials of the Khovanov homology of cables. We also obtain a conjectural closed formula for the Poincaré series of the skein lasagna module of $\overline{\mathbb{CP}^2}$. Accompanying this note is an online database of colored superpolynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03916 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computing colored Khovanov homology von Merkl, Karim Ritter Quantum Algebra Geometric Topology We compare eight versions of finite-dimensional categorifications of the colored Jones polynomial and show that they yield isomorphic results over a field of characteristic zero. As an application, we verify a physics-motivated conjectural formula for colored superpolynomials based on Poincaré polynomials of the Khovanov homology of cables. We also obtain a conjectural closed formula for the Poincaré series of the skein lasagna module of $\overline{\mathbb{CP}^2}$. Accompanying this note is an online database of colored superpolynomials. |
| title | Computing colored Khovanov homology |
| topic | Quantum Algebra Geometric Topology |
| url | https://arxiv.org/abs/2505.03916 |