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

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

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


Authors

Andrew Monaghan

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
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

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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.





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