Non-compact Riemann surfaces are equilaterally triangulable
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866909795357818880 |
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| author | Bishop, Christopher J. Rempe, Lasse |
| author_facet | Bishop, Christopher J. Rempe, Lasse |
| contents | We show that every open Riemann surface can be obtained by glueing together a countable collection of equilateral triangles, in such a way that every vertex belongs to finitely many triangles. Equivalently, it is a _Belyi surface_: There exists a holomorphic branched covering to the Riemann sphere that is branched only over three values. It follows that every Riemann surface is a branched cover of the sphere, branched only over finitely many points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_16702 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Non-compact Riemann surfaces are equilaterally triangulable Bishop, Christopher J. Rempe, Lasse Complex Variables Algebraic Geometry Differential Geometry Dynamical Systems Primary 30F20, Secondary 14H57, 30D05, 30F60, 32G15, 37F10, 37F30 We show that every open Riemann surface can be obtained by glueing together a countable collection of equilateral triangles, in such a way that every vertex belongs to finitely many triangles. Equivalently, it is a _Belyi surface_: There exists a holomorphic branched covering to the Riemann sphere that is branched only over three values. It follows that every Riemann surface is a branched cover of the sphere, branched only over finitely many points. |
| title | Non-compact Riemann surfaces are equilaterally triangulable |
| topic | Complex Variables Algebraic Geometry Differential Geometry Dynamical Systems Primary 30F20, Secondary 14H57, 30D05, 30F60, 32G15, 37F10, 37F30 |
| url | https://arxiv.org/abs/2103.16702 |