{
  "abstract": "Suppose that $M$ is a finite-volume cusped hyperbolic three-manifold, equipped with a veering triangulation $\\mathcal{V}$. We prove that the action of the fundamental group of $M$ on the veering two-sphere is a geometrically finite convergence action. Applying a result of Yaman, we deduce that the veering two-sphere is equivariantly homeomorphic to the boundary of hyperbolic space. As an application, we obtain Cannon-Thurston maps associated to veering triangulations. If $\\mathcal{V}$ is layered we recover the classical Cannon-Thurston map. If it is not we obtain Cannon-Thurston maps that do not come from surface subgroups. These are the first such examples in the cusped case. Finally, we implement an algorithm to draw approximations of these Cannon-Thurston maps. This improves upon previous approximations obtained by Thurston and others.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14598",
  "author_total": 3,
  "authors": [
    {
      "name": "Jason Fox Manning"
    },
    {
      "name": "Saul Schleimer"
    },
    {
      "name": "Henry Segerman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d97y7w69tz16r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14598",
  "fulltext_url": null,
  "id": "d97y7w69tz16r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14598",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7213367997",
  "pdf_url": "https://arxiv.org/pdf/2609.14598",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d97y7w69tz16r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14598",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14598"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "From veering triangulations to convergence actions and back again",
  "title_text": "From veering triangulations to convergence actions and back again",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/d97y7w69tz16r",
  "venue": "arXiv",
  "versions": []
}