{
  "abstract": "We prove that every representation of a closed surface group of genus at least $3$ into $\\mathrm{PSL}(2,\\mathbb{R})$ that is sufficiently close (but not equal to) a representation that has non-compact solvable image has a simple closed separating curve that is mapped to a non-trivial elliptic element in $\\mathrm{PSL}(2,\\mathbb{R})$. This can be seen as evidence for an affirmative answer to a question of Bowditch and a conjecture of Goldman.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40040",
  "author_total": 3,
  "authors": [
    {
      "name": "Marit Bobb"
    },
    {
      "name": "James Farre"
    },
    {
      "name": "Peter Smillie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/enj3hrvxb15nc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40040",
  "fulltext_url": null,
  "id": "enj3hrvxb15nc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40040",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40040",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/enj3hrvxb15nc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40040",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40040"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The Torelli Group and Euler Class Zero $\\mathrm{PSL}(2,\\mathbb{R})$ Representations",
  "title_text": "The Torelli Group and Euler Class Zero PSL(2,ℝ) Representations",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/enj3hrvxb15nc",
  "venue": "arXiv",
  "versions": []
}