On countability of Teichmüller modular groups for analytically infinite Riemann surfaces defined by generalized Cantor sets
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914865064443904 |
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| author | Kinjo, Erina |
| author_facet | Kinjo, Erina |
| contents | For any analytically finite Riemann surface, the Teichmüller modular group is countable, but it is not easy to find an analytically infinite Riemann surface for which the Teichmüller modular group is countable. In this paper, we show that the Teichmüller modular group is countable or uncountable for some analytically infinite Riemann surfaces defined by generalized Cantor sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07533 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On countability of Teichmüller modular groups for analytically infinite Riemann surfaces defined by generalized Cantor sets Kinjo, Erina Complex Variables Primary 30F60, Secondary 32G15 For any analytically finite Riemann surface, the Teichmüller modular group is countable, but it is not easy to find an analytically infinite Riemann surface for which the Teichmüller modular group is countable. In this paper, we show that the Teichmüller modular group is countable or uncountable for some analytically infinite Riemann surfaces defined by generalized Cantor sets. |
| title | On countability of Teichmüller modular groups for analytically infinite Riemann surfaces defined by generalized Cantor sets |
| topic | Complex Variables Primary 30F60, Secondary 32G15 |
| url | https://arxiv.org/abs/2407.07533 |