Non-arithmeticity of length spectra of subgroups of mapping class groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917490666242048 |
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| author | Choi, Inhyeok Kim, Dongryul M. |
| author_facet | Choi, Inhyeok Kim, Dongryul M. |
| contents | In this paper, we prove that every non-elementary subgroup of the mapping class group of a surface has non-arithmetic Teichmüller length spectrum. Namely, Teichmüller translation lengths of its pseudo-Anosov elements generate a dense additive subgroup of $\mathbb{R}$. We prove this by introducing the notion of cross-ratios on $\mathcal{MF}$ and $\mathcal{PMF}$, and studying its geometric and dynamical properties, despite the lack of negatively curved features of the Teichmüller space nor the conformal geometry on $\mathcal{PMF}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13064 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-arithmeticity of length spectra of subgroups of mapping class groups Choi, Inhyeok Kim, Dongryul M. Geometric Topology Dynamical Systems Group Theory In this paper, we prove that every non-elementary subgroup of the mapping class group of a surface has non-arithmetic Teichmüller length spectrum. Namely, Teichmüller translation lengths of its pseudo-Anosov elements generate a dense additive subgroup of $\mathbb{R}$. We prove this by introducing the notion of cross-ratios on $\mathcal{MF}$ and $\mathcal{PMF}$, and studying its geometric and dynamical properties, despite the lack of negatively curved features of the Teichmüller space nor the conformal geometry on $\mathcal{PMF}$. |
| title | Non-arithmeticity of length spectra of subgroups of mapping class groups |
| topic | Geometric Topology Dynamical Systems Group Theory |
| url | https://arxiv.org/abs/2605.13064 |