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Title: Complex hyperbolic triangle groups
Author: Monaghan, Andrew
Awarding Body: University of Liverpool
Current Institution: University of Liverpool
Date of Award: 2013
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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.
Supervisor: Pratoussevitch, Anna; Goryunov, Victor Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics