{
  "abstract": "Given a locally finite graph $Γ$, Udall proved that the mapping class group of the doubled handlebody associated to $Γ$ is an extension of the mapping class group of $Γ$ by a possibly infinite direct product of $\\mathbb{Z}_2$, and that this extension splits. We give a formula for Udall's section restricted to the pure mapping class group and, when $Γ$ has finitely many ends, on the whole mapping class group.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24912",
  "author_total": 1,
  "authors": [
    {
      "name": "Jorge Andres Robinson Arrieta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1e95jbaz7drvd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24912",
  "fulltext_url": null,
  "id": "1e95jbaz7drvd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24912",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7223064112",
  "pdf_url": "https://arxiv.org/pdf/2610.24912",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1e95jbaz7drvd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24912",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24912"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "An explicit section of the Laudenbach-type exact sequence of the big mapping class group of $M_Γ$",
  "title_text": "An explicit section of the Laudenbach-type exact sequence of the big mapping class group of M_Γ",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/1e95jbaz7drvd",
  "venue": "arXiv",
  "versions": []
}