Year: 2026
Type: preprint
Abstract: We generalize a method devised by Mark and Paupert for finding group presentations of the single-cusped standard Picard modular groups $\text{PU}(2, 1; \mathcal{O}_d)$, where $\mathcal{O}_d$ is the ring of integers of $\mathbb{Q}(i\sqrt{d})$, to a more general class of lattices in $\text{PU}(2, 1)$. As an application, we give presentations for the so-called \textit{sisters} of the standard Picard modular groups for $d=3, 7,$ and $11$. In particular, this shows that the sister of $\text{PU}(2, 1; \mathcal{O}_7)$ is a perfect group.
Source: arXiv (Cornell University)
Author: Young, Jackson
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224883123