Coordinates for ${\rm SL}_3$-web basis elements in closed surfaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918488820416512 |
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| author | Sun, Zhe Wang, Zhihao |
| author_facet | Sun, Zhe Wang, Zhihao |
| contents | The ${\rm SL}_3$-skein algebra of a closed surface $Σ_g$ is a quantization of the ${\rm SL}_3$ character variety of $Σ_g$, where $g$ denotes the genus of the surface. This algebra admits a basis consisting of non-elliptic web diagrams in $Σ_g$. In this paper, we introduce explicit coordinates for non-elliptic web diagrams on $Σ_g$, yielding a parametrization by a submonoid of $\mathbb Z^{d}$. Here $d = 16g - 16$ for $g \ge 2$ and $d = 4$ in the torus case $g = 1$, coinciding with the dimension of the corresponding character variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19445 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Coordinates for ${\rm SL}_3$-web basis elements in closed surfaces Sun, Zhe Wang, Zhihao Geometric Topology Quantum Algebra The ${\rm SL}_3$-skein algebra of a closed surface $Σ_g$ is a quantization of the ${\rm SL}_3$ character variety of $Σ_g$, where $g$ denotes the genus of the surface. This algebra admits a basis consisting of non-elliptic web diagrams in $Σ_g$. In this paper, we introduce explicit coordinates for non-elliptic web diagrams on $Σ_g$, yielding a parametrization by a submonoid of $\mathbb Z^{d}$. Here $d = 16g - 16$ for $g \ge 2$ and $d = 4$ in the torus case $g = 1$, coinciding with the dimension of the corresponding character variety. |
| title | Coordinates for ${\rm SL}_3$-web basis elements in closed surfaces |
| topic | Geometric Topology Quantum Algebra |
| url | https://arxiv.org/abs/2602.19445 |