{
  "abstract": "For punctured surfaces $Σ_{g,p}$ of genus $g\\geqslant 2$, we explore the dynamics of the mapping class group action on the relative $\\mathrm{PSL}(2,\\mathbb{R})$-character varieties of type-preserving representations. For such relative character varieties, Goldman's conjecture predicts that the mapping class group acts ergodically on their non-Teichmüller components. A related question of Bowditch asks whether every non-elementary type-preserving representation that is non-Fuchsian sends some non-peripheral simple closed curve to a non-hyperbolic element. We show that, on the components of the relative character variety indexed by fixed signs of images of peripheral elements and relative Euler classes non-extremal in the generalized Milnor-Wood inequality, an affirmative answer to Bowditch's question implies Goldman's conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02065",
  "author_total": 2,
  "authors": [
    {
      "name": "Viraj Joshi"
    },
    {
      "name": "Inyoung Ryu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6b5k3fd3z2f5h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02065",
  "fulltext_url": null,
  "id": "6b5k3fd3z2f5h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02065",
  "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": "W7207714214",
  "pdf_url": "https://arxiv.org/pdf/2609.02065",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6b5k3fd3z2f5h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.02065",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02065"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "From Bowditch question to Goldman conjecture for type-preserving representations",
  "title_text": "From Bowditch question to Goldman conjecture for type-preserving representations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/6b5k3fd3z2f5h",
  "venue": "arXiv",
  "versions": []
}