{
  "abstract": "We show that non-Fuchsian geometrically finite hyperbolic structures on a given hyperbolizable 3-manifold M are uniquely determined, up to isotopy, by their bending laminations. Consequently, the bending map from the space of non-Fuchsian geometrically finite structures on M, endowed with the strong topology, to the space of bending laminations, endowed with Lecuire's tubular topology, is a homeomorphism. This extends the convex co-compact case established with Schlenker. The proof combines hyperbolic Dehn filling, continuity and properness of the bending map (Lecuire) and real-analyticity of its fibres (Bonahon). We also establish a criterion for contractibility of the boundary fibres of a continuous extension of a homeomorphism, extending Finney's theorem to a boundary setting. This topological result may be of independent interest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29450",
  "author_total": 1,
  "authors": [
    {
      "name": "Bruno Dular"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7mb4p1rrgymg1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29450",
  "fulltext_url": null,
  "id": "7mb4p1rrgymg1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29450",
  "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.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7214358385",
  "pdf_url": "https://arxiv.org/pdf/2609.29450",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7mb4p1rrgymg1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29450",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29450"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Bending parameterization of geometrically finite hyperbolic manifolds",
  "title_text": "Bending parameterization of geometrically finite hyperbolic manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/7mb4p1rrgymg1",
  "venue": "arXiv",
  "versions": []
}