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

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

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
• Electronic ISSN: 1469-7750
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 100
• Issue: 2
• Pages: 545-567
• DOI: https://doi.org/10.1112/jlms.12227
• Public URL: https://durham-repository.worktribe.com/output/1303192
• Related Public URLs: https://arxiv.org/abs/1807.03211