{
  "abstract": "We prove the following ``Torus Trichotomy Theorem'': every finitely generated subgroup of $\\pls$ is either virtually free, a central extension of a cocompact Fuchsian group by a finite cyclic group, or a one-ended, non-acylindrically-hyperbolic group containing $\\mathbb{Z}^2$. In particular, we obtain the ``free or surface'' alternative for word-hyperbolic groups of PL homeomorphisms of the circle.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.12168",
  "author_total": 4,
  "authors": [
    {
      "name": "Leonardo Dinamarca"
    },
    {
      "name": "Maximiliano Escayola"
    },
    {
      "name": "Sang-hyun Kim"
    },
    {
      "name": "Thomas Koberda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e89qxwpwd4dpj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.12168",
  "fulltext_url": null,
  "id": "e89qxwpwd4dpj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.12168",
  "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.DS"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7203504181",
  "pdf_url": "https://arxiv.org/pdf/2608.12168",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e89qxwpwd4dpj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2608.12168",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.12168"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Hyperbolicity and obstructions to PL actions of the circle",
  "title_text": "Hyperbolicity and obstructions to PL actions of the circle",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/e89qxwpwd4dpj",
  "venue": "arXiv",
  "versions": []
}