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Torsion in 1-cusped Picard modular groups
- Publication Year :
- 2022
-
Abstract
- We present a systematic effective method to construct coarse fundamental domains for the action of the Picard modular groups $PU(2,1,\mathcal{O}_d)$ where $\mathcal{O}_d$ has class number one, i.e. $d=1,2,3,7,11,19,43,67,163$. The computations can be performed quickly up to the value $d=19$. As an application of this method, we classify conjugacy classes of torsion elements, deduce short presentations for the groups, and construct neat subgroups of small index.
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2205.03037
- Document Type :
- Working Paper