Algebraic Mapping Class Group Rigidity

Seong Youn Kim

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arXiv · 2508.09421

Algebraic Mapping Class Group Rigidity

Seong Youn Kim

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Abstract

Let $g, n \geq 0$ and $\Sigma = \Sigma_{g, n}$ be a connected oriented surface of genus $g$ with $n$ punctures. The $\mathrm{SL}_2$-character variety of $\Sigma$ has a rigid relative automorphism group, whose elements fix each monodromies along punctures, and is a finite extension of the mapping class group. The exceptional isomorphism between the $\mathrm{SL}(2, \mathbb{C})$-character variety and moduli of points on complex $3$-sphere provides a new description of the mapping class group of certain $\Sigma$.

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Seong Youn Kim. 2025-08-13. Algebraic Mapping Class Group Rigidity. https://arxiv.org/abs/2508.09421

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