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| Format: | Preprint |
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2019
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| Online Access: | https://arxiv.org/abs/1905.02002 |
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| _version_ | 1866917891639607296 |
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| author | Maluendas, Camilo Ramírez |
| author_facet | Maluendas, Camilo Ramírez |
| contents | In this paper, we study the PSV construction, which provides a step by step method for obtaining tame translation surfaces with a suitable Veech group. In addition, we modify slightly this construction, and for each finitely generated subgroup $G<{\rm GL}_{+}(2,\mathbb{R})$ without contracting elements, we produce a tame translation surface $S$ with infinite genus such that its Veech group is $G$. Furthermore, the ends space of $S$ can be written as $\mathcal{B}\sqcup \mathcal{U}$, where $\mathcal{B}$ is homeomorphic to the ends space of the group $G$, and $\mathcal{U}$ is a countable, discrete, dense, and open subset of the ends space of $S$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1905_02002 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | On the Ends of groups and the Veech groups of infinite-genus surfaces Maluendas, Camilo Ramírez Differential Geometry 05C3, 05C25, 52B15, 05C07 In this paper, we study the PSV construction, which provides a step by step method for obtaining tame translation surfaces with a suitable Veech group. In addition, we modify slightly this construction, and for each finitely generated subgroup $G<{\rm GL}_{+}(2,\mathbb{R})$ without contracting elements, we produce a tame translation surface $S$ with infinite genus such that its Veech group is $G$. Furthermore, the ends space of $S$ can be written as $\mathcal{B}\sqcup \mathcal{U}$, where $\mathcal{B}$ is homeomorphic to the ends space of the group $G$, and $\mathcal{U}$ is a countable, discrete, dense, and open subset of the ends space of $S$. |
| title | On the Ends of groups and the Veech groups of infinite-genus surfaces |
| topic | Differential Geometry 05C3, 05C25, 52B15, 05C07 |
| url | https://arxiv.org/abs/1905.02002 |