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

Povall, Sam; Pratoussevitch, Anna

doi:10.1090/ecgd/348

Complex hyperbolic triangle groups of type $[m,m,0;3,3,2]$
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by Sam Povall and Anna Pratoussevitch PDF

Conform. Geom. Dyn. 24 (2020), 51-67 Request permission

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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