{
  "abstract": "We construct a modular operad $\\mathbf{S}$ of mapping class groupoids modelling the higher-genus Teichmüller tower, with compositions and contractions encoding surface gluing. We prove a presentation theorem for maps out of $\\mathbf{S}$ using genus-zero and genus-one generators and relations. Applying the work of Nakamura--Schneps, we obtain a faithful action of their subgroup $\\widehatΓ\\subseteq \\widehat{\\mathsf{GT}}$ on $\\widehat{\\mathbf{S}}$, and hence a faithful Galois action. The genus-zero truncation identifies with the cyclic operad of parenthesized ribbon braids, whose object-fixing profinite automorphism group is $\\widehat{\\mathsf{GT}}$. The completed classifying spaces form a modular $\\infty$-operad whose corolla values are geometric étale homotopy types of moduli stacks of curves with nonzero tangent vectors at their marked points. The $\\widehatΓ$-action induces a faithful action by homotopy automorphisms on the associated tower of profinite homotopy $1$-types, which agrees with the étale model in genus zero and one.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.01466",
  "author_total": 2,
  "authors": [
    {
      "name": "Luciana Basualdo Bonatto"
    },
    {
      "name": "Marcy Robertson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0zagmaj5tvcfs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.01466",
  "fulltext_url": null,
  "id": "0zagmaj5tvcfs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.01466",
  "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.AT"
    ],
    [
      "arxiv",
      "math.CT"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7163147834",
  "pdf_url": "https://arxiv.org/pdf/2606.01466",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0zagmaj5tvcfs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2606.01466",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.01466"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Galois actions on surfaces and a higher genus Grothendieck-Teichmüller group",
  "title_text": "Galois actions on surfaces and a higher genus Grothendieck-Teichmüller group",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/0zagmaj5tvcfs",
  "venue": "arXiv",
  "versions": []
}