Complex hyperbolic triangle groups



Monaghan, Andrew
Complex hyperbolic triangle groups. [Unspecified]

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Abstract

In this thesis we study the discreteness criteria for complex hyperbolic triangle groups, generated by reflections in the complex hyperbolic 2-space. A complex hyperbolic triangle group is a group of isometries of the complex hyperbolic plane generated by three complex reflections. We study discreteness of some of these groups using arithmetic and geometric methods. We show that certain complex hyperbolic triangle groups of signature (p,p,2p) and (p,q,pq/(q-p)) are not discrete. The arithmetic methods we use are those studied by Conway and Jones and Parker. We also extend these results further. We finally give an area of discreteness for complex hyperbolic triangle groups of signature [m,n,0] using the compression property.

Item Type: Unspecified
Additional Information: Date: 2013-10 (completed)
Uncontrolled Keywords: complex hyperbolic triangle groups
Subjects: Q Science > QA Mathematics
Divisions: ?? dep_math ??
Depositing User: Symplectic Admin
Date Deposited: 31 Jul 2014 10:33
Last Modified: 09 Jan 2021 08:54
URI: https://livrepository.liverpool.ac.uk/id/eprint/14033