{
  "abstract": "The Squier complex $\\mathcal{D}(\\cP)$ has been defined in \\cite{LDHM1} as a combinatorial 2-complex. Also several extensions of $\\mathcal{D}(\\cP)$ are defined and used extensively in \\cite{LDHM2}, \\cite{SES} and \\cite{EP}. Since the results obtained in those papers rely on the assumption that $\\mathcal{D}(\\cP)$ and its extensions in \\cite{LDHM2} and \\cite{SES} are CW-complexes of dimensions 2 and 3, respectively, and no proofs are given to support these preconditions, we provide the respective proofs in the present paper.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03608",
  "author_total": 1,
  "authors": [
    {
      "name": "Elton Pasku"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fr9eawscgbtya.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03608",
  "fulltext_url": null,
  "id": "fr9eawscgbtya",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03608",
  "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.AT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7220424026",
  "pdf_url": "https://arxiv.org/pdf/2610.03608",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fr9eawscgbtya.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.03608",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03608"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The Squire complex and its extensions revisited",
  "title_text": "The Squire complex and its extensions revisited",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/fr9eawscgbtya",
  "venue": "arXiv",
  "versions": []
}