Complex Hyperbolic Triangle Groups of Type $[m,m,0;3,3,2]$

Sam Povall; Anna Pratoussevitch

doi:10.1090/ecgd/348

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arXiv · 1901.01572

Complex Hyperbolic Triangle Groups of Type $[m,m,0;3,3,2]$

Sam Povall·Anna Pratoussevitch

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Abstract

In this paper we study discreteness of complex hyperbolic triangle groups of type $[m,m,0;3,3,2]$, i.e. groups of isometries of the complex hyperbolic plane generated by three complex reflections of orders $3,3,2$ 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 intervals in this parameter space that correspond to discrete and to non-discrete triangle groups.

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Sam Povall, Anna Pratoussevitch. 2019-01-06. Complex Hyperbolic Triangle Groups of Type $[m,m,0;3,3,2]$. https://doi.org/10.1090/ecgd%2F348

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