Work

Discreteness of ultra‐parallel complex hyperbolic triangle groups of type [m1,m2,0]

Year: 2019

Type: article

Abstract: In this paper, we consider ultra-parallel complex hyperbolic triangle groups of type [ m 1 , m 2 , 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.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.12227

Authors: Andrew Monaghan, John R. Parker, Anna Pratoussevitch

Institutions: University of Liverpool, Durham University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Engineering and Physical Sciences Research Council

Awards: RNMS: Geometric structures and representation varieties, RNMS: Geometric Structures and Representation Varieties, RNMS: Geometric Structures and Representation Varieties