English

Torsion in 1-cusped Picard modular groups

Algebraic Geometry 2022-11-22 v3 Differential Geometry Geometric Topology

Abstract

We present a systematic effective method to construct coarse fundamental domains for the action of the Picard modular groups PU(2,1,Od)PU(2,1,\mathcal{O}_d) where Od\mathcal{O}_d has class number one, i.e. d=1,2,3,7,11,19,43,67,163d=1,2,3,7,11,19,43,67,163. The computations can be performed quickly up to the value d=19d=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.

Cite

@article{arxiv.2205.03037,
  title  = {Torsion in 1-cusped Picard modular groups},
  author = {Martin Deraux and Mengmeng Xu},
  journal= {arXiv preprint arXiv:2205.03037},
  year   = {2022}
}
R2 v1 2026-06-24T11:08:58.799Z