Non-discrete complex hyperbolic $(p_1,p_2,p_3;p_4)$-triangle groups

In this paper, we study complex hyperbolic triangle groups of type $(p_1,p_2,p_3;p_4)$ with $3\le p_1\le p_2\le p_3\le p_4\le \infty$. 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.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-26
DOI
https://doi.org/10.48550/arxiv.2610.35197
Primary Topic
Geometric and Algebraic Topology
Type
preprint
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preprint

Non-discrete complex hyperbolic $(p_1,p_2,p_3;p_4)$-triangle groups

John R. Parker, Wei Liao
arXiv (Cornell University)
Geometric and Algebraic Topology
preprint

Non-discrete complex hyperbolic $(p_1,p_2,p_3;p_4)$-triangle groups

John R. Parker, Wei Liao
preprint en

Abstract

In this paper, we study complex hyperbolic triangle groups of type $(p_1,p_2,p_3;p_4)$ with $3\le p_1\le p_2\le p_3\le p_4\le \infty$. 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.

arXiv (Cornell University)
Geometric and Algebraic Topology
DOIOpen Access PDFOpenAlex
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Non-discrete complex hyperbolic $(p_1,p_2,p_3;p_4)$-triangle groups — John R. Parker, Wei Liao · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS