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

Monaghan, Andrew, Parker, John R and Pratoussevitch, Anna ORCID: 0000-0003-2248-6382 Discreteness of Ultra-Parallel Complex Hyperbolic Triangle Groups of Type $[m_1,m_2,0]$.

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Abstract

In this paper we consider ultra-parallel complex hyperbolic triangle groups of type $[m_1,m_2,0]$, i.e. 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
Additional Information:	23 pages, 4 figures
Uncontrolled Keywords:	math.GT, math.GT, Primary 51M10, Secondary 32M15, 22E40, 53C55
Depositing User:	Symplectic Admin
Date Deposited:	16 Jul 2018 15:38
Last Modified:	19 Jan 2023 01:30
Related URLs:	Author
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3023652

Available Versions of this Item

• Discreteness of Ultra-Parallel Complex Hyperbolic Triangle Groups of Type $[m_1,m_2,0]$. (deposited 16 Jul 2018 15:38) [Currently Displayed]
  • Discreteness of Ultra-Parallel Complex Hyperbolic Triangle Groups of Type [m1,m2,0]. (deposited 29 Apr 2019 07:53)