On the structure of Kauffman bracket skein algebra of a surface
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917684518584320 |
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| author | Chen, Haimiao |
| author_facet | Chen, Haimiao |
| contents | Suppose $R$ is a commutative ring with identity and a fixed invertible element $q^{\frac{1}{2}}$ such that $q+q^{-1}$ is invertible.
For an oriented surface $Σ$, let $\mathcal{S}(Σ;R)$ denote the Kauffman bracket skein algebra of $Σ$ over $R$. It is shown that to each embedded graph $G\subsetΣ$ satisfying that $Σ\setminus G$ is homeomorphic to a disk and some other mild conditions, one can associate a generating set for $\mathcal{S}(Σ;R)$, and the ideal of defining relations is generated by relations of degree at most $6$ supported by certain small subsurfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02299 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the structure of Kauffman bracket skein algebra of a surface Chen, Haimiao Geometric Topology Quantum Algebra 57K16, 57K31 Suppose $R$ is a commutative ring with identity and a fixed invertible element $q^{\frac{1}{2}}$ such that $q+q^{-1}$ is invertible. For an oriented surface $Σ$, let $\mathcal{S}(Σ;R)$ denote the Kauffman bracket skein algebra of $Σ$ over $R$. It is shown that to each embedded graph $G\subsetΣ$ satisfying that $Σ\setminus G$ is homeomorphic to a disk and some other mild conditions, one can associate a generating set for $\mathcal{S}(Σ;R)$, and the ideal of defining relations is generated by relations of degree at most $6$ supported by certain small subsurfaces. |
| title | On the structure of Kauffman bracket skein algebra of a surface |
| topic | Geometric Topology Quantum Algebra 57K16, 57K31 |
| url | https://arxiv.org/abs/2406.02299 |