Algebraic generators of the skein algebra of a surface

Ramanujan Santharoubane

doi:10.2140/agt.2024.24.2571

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arXiv · 1803.09804

Algebraic generators of the skein algebra of a surface

Ramanujan Santharoubane

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Abstract

Let $\Sigma$ be a surface with negative Euler characteristic, genus at least one and at most one boundary component. We prove that the skein algebra of $\Sigma$ 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 $\Sigma$. 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 $\Sigma$.

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Ramanujan Santharoubane. 2018-03-26. Algebraic generators of the skein algebra of a surface. https://doi.org/10.2140/agt.2024.24.2571

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