{
  "abstract": "We give conditions ensuring that an asymptotically rigid mapping class group, specifically a surface Houghton group $\\mathcal{H}(S)$, has finite index in the asymptotically conformal modular group $\\text{Mod}_0(X)$, where $X$ is a hyperbolic structure on $S$. These include geometric conditions on the pieces of the underlying rigid structure, as well as the existence in $\\mathcal{H}(S)$ of an end-periodic homeomorphism which is asymptotically conformal. As a consequence, if $S$ has $n\\geq 3$ ends, then $\\text{Mod}_0(X)$ has type $F_{n-1}$ but not $FP_n$. We also establish analogous results for $L^p$ modular groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08849",
  "author_total": 3,
  "authors": [
    {
      "name": "Javier Aramayona"
    },
    {
      "name": "George Domat"
    },
    {
      "name": "Christopher Leininger"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/504tqn5wh4ykv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08849",
  "fulltext_url": null,
  "id": "504tqn5wh4ykv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08849",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7212076781",
  "pdf_url": "https://arxiv.org/pdf/2609.08849",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/504tqn5wh4ykv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:01Z",
      "native_id": "2609.08849",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08849"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Asymptotically conformal and asymptotically rigid mapping class groups",
  "title_text": "Asymptotically conformal and asymptotically rigid mapping class groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:01Z",
  "url": "https://research.draconitic.com/paper/504tqn5wh4ykv",
  "venue": "arXiv",
  "versions": []
}