Monaghan, Andrew
Complex hyperbolic triangle groups.
Doctor of Philosophy thesis, University of Liverpool.
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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: | Thesis (Doctor of Philosophy) |
|---|---|
| Additional Information: | Date: 2013-10 (completed) |
| Uncontrolled Keywords: | complex hyperbolic triangle groups |
| Subjects: | ?? QA ?? |
| Divisions: | Faculty of Science and Engineering > School of Physical Sciences > Mathematical Sciences |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 31 Jul 2014 10:33 |
| Last Modified: | 16 Dec 2022 04:41 |
| DOI: | 10.17638/00014033 |
| Supervisors: |
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| URI: | https://livrepository.liverpool.ac.uk/id/eprint/14033 |
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