Teichm\"{u}ller isometries induced by certain irreducible periodic mapping classes

Atreyee Bhattacharya; Satyajit Maity; Kashyap Rajeevsarathy

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arXiv · 2606.13009

Teichm\"{u}ller isometries induced by certain irreducible periodic mapping classes

Atreyee Bhattacharya·Satyajit Maity·Kashyap Rajeevsarathy

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Abstract

Let $\mathrm{Mod}(S_g)$ be the mapping class group of the closed orientable surface of genus $g \geq 2$, and let $\mathrm{Teich}(S_g)$ be the Teichm\"{u}ller space of $S_g$. In this paper, we provide an algorithm for determining the isometries induced in $\mathrm{Teich}(S_g)$ by certain irreducible periodic mapping classes in Fenchel-Nielsen coordinates. As a demonstration of this method, we provide a description of the isometry induced by periodic mapping class of order $4g+2$ and also derive some of its geometric properties.

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Atreyee Bhattacharya, Satyajit Maity, Kashyap Rajeevsarathy. 2026-06-11. Teichm\"{u}ller isometries induced by certain irreducible periodic mapping classes. https://arxiv.org/abs/2606.13009

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