{
  "abstract": "We give a presentation of a groupoid of transformations of quilt decompositions of a surface, which are pants decompositions of the surface with the addition of \"seams\". We consider colored quilt decompositions of a surface, where one side of a quilt decomposition is colored. We also give a presentation of a groupoid of transformations of colored quilt decompositions of a surface. These presentations of such groupoids are realized by constructing connected and simply-connected two-dimensional cell complexes whose 0-cell are these up-to-isotopy structures on the surface. In the latter part of this paper, we show that Torelli group (or more precisely, a torsion-free subgroup of a mapping class group of a surface) acts on these complexes freely.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02974",
  "author_total": 1,
  "authors": [
    {
      "name": "Hiromasa Fuchizawa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/51ba9j6nkdz0g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02974",
  "fulltext_url": null,
  "id": "51ba9j6nkdz0g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02974",
  "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.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7208751468",
  "pdf_url": "https://arxiv.org/pdf/2609.02974",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/51ba9j6nkdz0g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2609.02974",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02974"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Quilt decompositions of surfaces and Torelli group action on the extended Hatcher complex",
  "title_text": "Quilt decompositions of surfaces and Torelli group action on the extended Hatcher complex",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/51ba9j6nkdz0g",
  "venue": "arXiv",
  "versions": []
}