Algebraic generators of the skein algebra of a surface
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2018
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| _version_ | 1866916371316604928 |
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| author | Santharoubane, Ramanujan |
| author_facet | Santharoubane, Ramanujan |
| contents | Let $Σ$ be a surface with negative Euler characteristic, genus at least one and at most one boundary component. We prove that the skein algebra of $Σ$ over the field of rational functions can be algebraically generated by a finite number of simple closed curves that are naturally associated to certain generators of the mapping class group of $Σ$. The action of the mapping class group on the skein algebra gives canonical relations between these generators. From this, we conjecture a presentation for a skein algebra of $Σ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1803_09804 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Algebraic generators of the skein algebra of a surface Santharoubane, Ramanujan Geometric Topology Let $Σ$ be a surface with negative Euler characteristic, genus at least one and at most one boundary component. We prove that the skein algebra of $Σ$ over the field of rational functions can be algebraically generated by a finite number of simple closed curves that are naturally associated to certain generators of the mapping class group of $Σ$. The action of the mapping class group on the skein algebra gives canonical relations between these generators. From this, we conjecture a presentation for a skein algebra of $Σ$. |
| title | Algebraic generators of the skein algebra of a surface |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/1803.09804 |