Estimating the distances between hyperbolic structures in the moduli space
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866929720123195392 |
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| author | Bhattacharya, Atreyee Paul, Suman Rajeevsarathy, Kashyap |
| author_facet | Bhattacharya, Atreyee Paul, Suman Rajeevsarathy, Kashyap |
| contents | Let $\mathrm{Mod}(S_g)$ be the mapping class group of the closed orientable surface $S_g$ of genus $g\geq 2$. Given a finite subgroup $H$ of $\mathrm{Mod}(S_g)$, let $\mathrm{Fix}(H)$ be the set of all fixed points induced by the action of $H$ on the Teichmüller space $\mathrm{Teich}(S_g)$ of $S_g$. This paper provides a method to estimate the distance between the unique fixed points of certain irreducible cyclic actions on $S_g$. We begin by deriving an explicit description of a pants decomposition of $S_g$, the length of whose curves are bounded above by the Bers' constant. To obtain the estimate, our method then uses the quasi-isometry between $\mathrm{Teich}(S_g)$ and the pants graph $\mathcal{P}(S_g)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13629 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Estimating the distances between hyperbolic structures in the moduli space Bhattacharya, Atreyee Paul, Suman Rajeevsarathy, Kashyap Geometric Topology Primary 57K20, Secondary 57M60 Let $\mathrm{Mod}(S_g)$ be the mapping class group of the closed orientable surface $S_g$ of genus $g\geq 2$. Given a finite subgroup $H$ of $\mathrm{Mod}(S_g)$, let $\mathrm{Fix}(H)$ be the set of all fixed points induced by the action of $H$ on the Teichmüller space $\mathrm{Teich}(S_g)$ of $S_g$. This paper provides a method to estimate the distance between the unique fixed points of certain irreducible cyclic actions on $S_g$. We begin by deriving an explicit description of a pants decomposition of $S_g$, the length of whose curves are bounded above by the Bers' constant. To obtain the estimate, our method then uses the quasi-isometry between $\mathrm{Teich}(S_g)$ and the pants graph $\mathcal{P}(S_g)$. |
| title | Estimating the distances between hyperbolic structures in the moduli space |
| topic | Geometric Topology Primary 57K20, Secondary 57M60 |
| url | https://arxiv.org/abs/2502.13629 |