Fenchel-Nielsen coordinates of the branch loci of cyclic actions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917169470636032 |
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| author | Bhattacharya, Atreyee Maity, Satyajit Rajeevsarathy, Kashyap |
| author_facet | Bhattacharya, Atreyee Maity, Satyajit Rajeevsarathy, Kashyap |
| contents | Let $S_g$ be a closed, connected, and oriented smooth surface of genus $g\geq 2$. Let the mapping class group of $S_g$ be denoted by $\mathrm{Mod}(S_g)$ and the Teichmüller space of $S_g$ by $\mathrm{Teich}(S_g)$. It is known that $\mathrm{Mod}(S_g)$ acts by isometries on $\mathrm{Teich}(S_g)$ with respect to the Weil-Petersson metric. In this paper, we develop algorithms to describe the Fenchel-Nielsen coordinates of fixed points of the actions of certain finite cyclic subgroups of $\mathrm{Mod}(S_g)$ on $\mathrm{Teich}(S_g)$. As applications of these algorithms, we compute the Fenchel-Nielsen coordinates of the fixed points of three cyclic subgroups of orders $10$, $8$, and $4$, in $\mathrm{Mod}(S_2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21463 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fenchel-Nielsen coordinates of the branch loci of cyclic actions Bhattacharya, Atreyee Maity, Satyajit Rajeevsarathy, Kashyap Geometric Topology Primary 57K20, Secondary 57M60 Let $S_g$ be a closed, connected, and oriented smooth surface of genus $g\geq 2$. Let the mapping class group of $S_g$ be denoted by $\mathrm{Mod}(S_g)$ and the Teichmüller space of $S_g$ by $\mathrm{Teich}(S_g)$. It is known that $\mathrm{Mod}(S_g)$ acts by isometries on $\mathrm{Teich}(S_g)$ with respect to the Weil-Petersson metric. In this paper, we develop algorithms to describe the Fenchel-Nielsen coordinates of fixed points of the actions of certain finite cyclic subgroups of $\mathrm{Mod}(S_g)$ on $\mathrm{Teich}(S_g)$. As applications of these algorithms, we compute the Fenchel-Nielsen coordinates of the fixed points of three cyclic subgroups of orders $10$, $8$, and $4$, in $\mathrm{Mod}(S_2)$. |
| title | Fenchel-Nielsen coordinates of the branch loci of cyclic actions |
| topic | Geometric Topology Primary 57K20, Secondary 57M60 |
| url | https://arxiv.org/abs/2512.21463 |