Bounded ideal triangulations of infinite Riemann surfaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912225443184640 |
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| author | Whitney, Casey Saric, Dragomir |
| author_facet | Whitney, Casey Saric, Dragomir |
| contents | We introduce a notion of a bounded ideal triangulation of an infinite Riemann surface and parametrize Teichmüller spaces of infinite surfaces which allow bounded triangulations. We prove that our parametrization is real-analytic. Riemann surfaces with bounded geometry and countably many punctures belong to the class of surfaces with bounded ideal triangulations. In comparison, the Fenchel-Nielsen parametrization for surfaces with bounded geometry is not known, while the Fenchel-Nielsen parametrization for surfaces with bounded pants decompositions is known as a homeomorphism but it is not known whether it is real-analytic |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05590 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bounded ideal triangulations of infinite Riemann surfaces Whitney, Casey Saric, Dragomir Geometric Topology Complex Variables We introduce a notion of a bounded ideal triangulation of an infinite Riemann surface and parametrize Teichmüller spaces of infinite surfaces which allow bounded triangulations. We prove that our parametrization is real-analytic. Riemann surfaces with bounded geometry and countably many punctures belong to the class of surfaces with bounded ideal triangulations. In comparison, the Fenchel-Nielsen parametrization for surfaces with bounded geometry is not known, while the Fenchel-Nielsen parametrization for surfaces with bounded pants decompositions is known as a homeomorphism but it is not known whether it is real-analytic |
| title | Bounded ideal triangulations of infinite Riemann surfaces |
| topic | Geometric Topology Complex Variables |
| url | https://arxiv.org/abs/2502.05590 |