{
  "abstract": "We present discrete, faithful and purely loxodromic representations of a closed surface group of genus 431, and of a free group, into the group of isometries of a finite-dimensional real-hyperbolic space for which no Cannon--Thurston map exists. The construction combines three ingredients: the small-cancellation strategy employed by Baker--Riley to construct a subgroup of an ambient hyperbolic group with no Cannon--Thurston map, the realization of these groups by octagon complexes, and a theorem of Desgroseilliers--Haglund that supplies a convex cocompact faithful representation of the ambient hyperbolic group on a real-hyperbolic space. These examples admit ray Cannon--Thurston maps, as defined by Halder, Mahan Mj and Sardar.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03855",
  "author_total": 1,
  "authors": [
    {
      "name": "Bruno Dular"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cnhkpf93s1qbq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03855",
  "fulltext_url": null,
  "id": "cnhkpf93s1qbq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03855",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03855",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cnhkpf93s1qbq.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.03855",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03855"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A surface-group action on real-hyperbolic space with no Cannon--Thurston map",
  "title_text": "A surface-group action on real-hyperbolic space with no Cannon--Thurston map",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/cnhkpf93s1qbq",
  "venue": "arXiv",
  "versions": []
}