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Discreteness of ultra-parallel complex hyperbolic triangle groups of type [m_1,m_2,0].

Monaghan, Andrew and Parker, John R. and Pratoussevitch, Anna (2019) 'Discreteness of ultra-parallel complex hyperbolic triangle groups of type [m_1,m_2,0].', Journal of the London Mathematical Society., 100 (2). pp. 545-567.


In this paper, we consider ultra‐parallel complex hyperbolic triangle groups of type [m1,m2,0] , that is, groups of isometries of the complex hyperbolic plane, generated by complex reflections in three ultra‐parallel complex geodesics two of which intersect on the boundary. We prove some discreteness and non‐discreteness results for these groups and discuss the connection between the discreteness results and ellipticity of certain group elements.

Item Type:Article
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Publisher statement:This is the accepted version of the following article: Monaghan, Andrew, Parker, John R. & Pratoussevitch, Anna (2019). Discreteness of Ultra-Parallel Complex Hyperbolic Triangle Groups of Type [m_1,m_2,0]. Journal of the London Mathematical Society 100(2): 545-567 which has been published in final form at This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.
Date accepted:24 April 2019
Date deposited:10 May 2019
Date of first online publication:14 May 2019
Date first made open access:10 May 2019

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