Complex Hyperbolic Triangle Groups of Type $[m,m,0; n_1, n_2, 2]$
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866913449051684864 |
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| author | Povall, Sam Pratoussevitch, Anna |
| author_facet | Povall, Sam Pratoussevitch, Anna |
| contents | In this paper we study the discreteness of complex hyperbolic triangle groups of type $[m,m,0; n_1, n_2, 2]$, i.e. groups of isometries of the complex hyperbolic plane generated by three complex reflections of orders $n_1, n_2, 2$ in complex geodesics with pairwise distances $m, m, 0$. For fixed $m$, the parameter space of such groups is of real dimension one. We determine the possible orders for $n_1$ and $n_2$ and also intervals in the parameter space that correspond to discrete and non-discrete triangle groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_02807 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Complex Hyperbolic Triangle Groups of Type $[m,m,0; n_1, n_2, 2]$ Povall, Sam Pratoussevitch, Anna Geometric Topology 51M10 (Primary) 32M15, 22E40, 53C55 (Secondary) In this paper we study the discreteness of complex hyperbolic triangle groups of type $[m,m,0; n_1, n_2, 2]$, i.e. groups of isometries of the complex hyperbolic plane generated by three complex reflections of orders $n_1, n_2, 2$ in complex geodesics with pairwise distances $m, m, 0$. For fixed $m$, the parameter space of such groups is of real dimension one. We determine the possible orders for $n_1$ and $n_2$ and also intervals in the parameter space that correspond to discrete and non-discrete triangle groups. |
| title | Complex Hyperbolic Triangle Groups of Type $[m,m,0; n_1, n_2, 2]$ |
| topic | Geometric Topology 51M10 (Primary) 32M15, 22E40, 53C55 (Secondary) |
| url | https://arxiv.org/abs/2101.02807 |