Discreteness of Ultra-Parallel Complex Hyperbolic Triangle Groups of Type [m_1,m_2,0]

Monaghan, Andrew; Parker, John R.; Pratoussevitch, Anna

doi:10.1112/jlms.12227

Discreteness of Ultra-Parallel Complex Hyperbolic Triangle Groups of Type [m_1,m_2,0]

Monaghan, Andrew; Parker, John R.; Pratoussevitch, Anna

Authors

Andrew Monaghan

Professor John Parker j.r.parker@durham.ac.uk
Professor

Anna Pratoussevitch

Abstract

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.

Citation

Monaghan, A., Parker, J. R., & Pratoussevitch, A. (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. https://doi.org/10.1112/jlms.12227

Journal Article Type	Article
Acceptance Date	Apr 24, 2019
Online Publication Date	May 14, 2019
Publication Date	Oct 31, 2019
Deposit Date	Apr 24, 2019
Publicly Available Date	May 10, 2019
Journal	Journal of the London Mathematical Society
Print ISSN	0024-6107
Publisher	Wiley
Peer Reviewed	Peer Reviewed
Volume	100
Issue	2
Pages	545-567
DOI	https://doi.org/10.1112/jlms.12227
Related Public URLs	https://arxiv.org/abs/1807.03211

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Copyright 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 https://doi.org/10.1112/jlms.12227. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.