{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35197",
  "author_total": 2,
  "authors": [
    {
      "name": "Wei Liao"
    },
    {
      "name": "John R Parker"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9dkgn2pv747ab.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35197",
  "fulltext_url": null,
  "id": "9dkgn2pv747ab",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35197",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7223965503",
  "pdf_url": "https://arxiv.org/pdf/2610.35197",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9dkgn2pv747ab.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35197",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35197"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Non-discrete complex hyperbolic $(p_1,p_2,p_3;p_4)$-triangle groups",
  "title_text": "Non-discrete complex hyperbolic (p_1,p_2,p_3;p_4)-triangle groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/9dkgn2pv747ab",
  "venue": "arXiv",
  "versions": []
}