Complex Hyperbolic Triangle Groups of Type $[m,m,0; n_1, n_2, 2]$

Sam Povall; Anna Pratoussevitch

Complex Hyperbolic Triangle Groups of Type $[m,m,0; n_1, n_2, 2]$

Geometric Topology 2024-07-30 v2

Authors: Sam Povall , Anna Pratoussevitch

Abstract

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.

Keywords

hyperbolic geometry hyperbolic groups

Cite

@article{arxiv.2101.02807,
  title  = {Complex Hyperbolic Triangle Groups of Type $[m,m,0; n_1, n_2, 2]$},
  author = {Sam Povall and Anna Pratoussevitch},
  journal= {arXiv preprint arXiv:2101.02807},
  year   = {2024}
}

Comments

34 pages, 2 figures. arXiv admin note: text overlap with arXiv:1901.01572

Complex Hyperbolic Triangle Groups of Type $[m,m,0; n_1, n_2, 2]$

Abstract

Keywords

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