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PreprintCC BY 4.0arXiv

Non-discrete complex hyperbolic (p1,p2,p3;p4)-triangle groups

  • Wei Liao
  • John R Parker
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Abstract

In this paper, we study complex hyperbolic triangle groups of type (p1,p2,p3;p4) with 3≤ p1≤ p2≤ p3≤ p4≤ ∞. We show that if the element R1R2R3 is elliptic, then the group is either non-discrete or it belongs to a short list of known discrete groups.

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Cite

BibTeXRIS
BibTeX
@misc{liao2026nondiscrete,
  title = {{Non-discrete complex hyperbolic $(p_1,p_2,p_3;p_4)$-triangle groups}},
  author = {Wei Liao and John R Parker},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35197},
  eprint = {2610.35197},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35197},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Non-discrete complex hyperbolic (p_1,p_2,p_3;p_4)-triangle groups
AU  - Wei Liao
AU  - John R Parker
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.35197
UR  - https://arxiv.org/abs/2610.35197
AB  - In this paper, we study complex hyperbolic triangle groups of type (p_1,p_2,p_3;p_4) with 3≤ p_1≤ p_2≤ p_3≤ p_4≤ ∞. We show that if the element R_1R_2R_3 is elliptic, then the group is either non-discrete or it belongs to a short list of known discrete groups.
ER  -