{
  "abstract": "We relate the theory of $q$-rational and $q$-real numbers introduced by Morier-Genoud and Ovsienko to the classical theory of Kleinian groups and their Teichmüller spaces. This provides a geometric point of view on several recent results about realisations of $q$-rationals for particular values of $ q \\in \\mathbb{C} $. As an application we resolve a conjecture of Bapat, Becker, and Licata on the topology of the $q$-deformed Farey tessellation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29831",
  "author_total": 1,
  "authors": [
    {
      "name": "Alex Elzenaar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0ycgsa1sr8nje.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29831",
  "fulltext_url": null,
  "id": "0ycgsa1sr8nje",
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  "landing_url": "https://arxiv.org/abs/2609.29831",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.QA"
    ],
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      "openalex",
      "2608|Geometric and Algebraic Topology"
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  "openalex": "W7214286222",
  "pdf_url": "https://arxiv.org/pdf/2609.29831",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0ycgsa1sr8nje.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.29831",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29831"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Quasi-Fuchsian groups and complex realisations of $q$-deformed real numbers",
  "title_text": "Quasi-Fuchsian groups and complex realisations of q-deformed real numbers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/0ycgsa1sr8nje",
  "venue": "arXiv",
  "versions": []
}