Complex hyperbolic triangle groups of type [m,m,0;3,3,2]

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 s...

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Bibliographic Details
Published in:Conformal geometry and dynamics 2020-02, Vol.24 (3), p.51-67
Main Authors: Povall, Sam, Pratoussevitch, Anna
Format: Article
Language:English
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Summary: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.
ISSN:1088-4173
1088-4173
DOI:10.1090/ecgd/348