Complex Hyperbolic Triangle Groups of Type [m,m,0; n₁, n₂, 2]

2021/01/08 by Sam Povall, Povall, Sam, Pratoussevitch, Anna
Mathematics · #22E40 #51M10 (Primary) 32M15 #53C55 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2101.02807

openalex publication_date 2021/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the discreteness of complex hyperbolic triangle groups of type [m,m,0; n₁, n₂, 2], i.e. groups of isometries of the complex hyperbolic plane generated by three complex reflections of orders n₁, n₂, 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 n₁ and n₂ and also intervals in the parameter space that correspond to discrete and non-discrete triangle groups.

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