Year: 2025
Type: preprint
Abstract: Let $g, n \geq 0$ and $Σ= Σ_{g, n}$ be a connected oriented surface of genus $g$ with $n$ punctures. The $\mathrm{SL}_2$-character variety of $Σ$ 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 $Σ$.
Source: arXiv (Cornell University)
Author: Kim, Seong Youn
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6891932138
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