Full metadata
Title
The Geometry of 1-cusped and 2-cusped Picard Modular Groups
Description
Mark and Paupert concocted a general method for producing presentations for arithmetic non-cocompact lattices, \(\Gamma\), in isometry groups of negatively curved symmetric spaces. To get around the difficulty of constructing fundamental domains in spaces of variable curvature, their method invokes a classical theorem of Macbeath applied to a \(\Gamma\)-invariant covering by horoballs of the negatively curved symmetric space upon which \(\Gamma\) acts. This thesis aims to explore the application of their method to the Picard modular groups, PU\((2,1;\mathcal{O}_{d})\), acting on \(\mathbb{H}_{\C}^2\). This document contains the derivations for the group presentations corresponding to \(d=2,11\), which completes the list of presentations for Picard modular groups whose entries lie in Euclidean domains, namely those with \(d=1,2,3,7,11\). There are differences in the method's application when the lattice of interest has multiple cusps. \(d = 5\) is the smallest value of \(d\) for which the corresponding Picard modular group, \(\PU(2,1;\mathcal{O}_5)\), has multiple cusps, and the method variations become apparent when working in this case.
Date Created
2021
Contributors
- Polletta, David Michael (Author)
- Paupert, Julien H (Thesis advisor)
- Kotschwar, Brett (Committee member)
- Fishel, Susanna (Committee member)
- Kawski, Matthias (Committee member)
- Childress, Nancy (Committee member)
- Arizona State University (Publisher)
Topical Subject
Extent
143 pages
Language
eng
Copyright Statement
In Copyright
Primary Member of
Peer-reviewed
No
Open Access
No
Handle
https://hdl.handle.net/2286/R.2.N.161554
Level of coding
minimal
Cataloging Standards
Note
Partial requirement for: Ph.D., Arizona State University, 2021
Field of study: Mathematics
System Created
- 2021-11-16 02:03:53
System Modified
- 2021-11-30 12:51:28
- 2 years 11 months ago
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