{
  "abstract": "A negative answer to Whitehead's asphericity problem would follow from an infinite chain of two-complexes, starting with a non-aspherical one, in which every inclusion induces the zero map on second homotopy groups. We prove that a connected two-complex $K$ is the first term of such chains of every \\emph{finite} length if and only if $K$ has a connected acyclic regular cover. In particular, there is a finite non-aspherical two-complex $K$, a presentation complex of $\\mathrm{SL}(2,5)$, such that for every $n$ there is a strictly increasing chain of finite two-complexes $K=K_0\\subset K_1\\subset\\dots\\subset K_n$ in which all inclusions are zero on $π_2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10074",
  "author_total": 2,
  "authors": [
    {
      "name": "Laurent Bartholdi"
    },
    {
      "name": "Roman Mikhailov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/as0zf0nmdfgkb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10074",
  "fulltext_url": null,
  "id": "as0zf0nmdfgkb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10074",
  "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.GR"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7220923162",
  "pdf_url": "https://arxiv.org/pdf/2610.10074",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/as0zf0nmdfgkb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.10074",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10074"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Finite Chains of Two-Complexes and Acyclic Covers",
  "title_text": "Finite Chains of Two-Complexes and Acyclic Covers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/as0zf0nmdfgkb",
  "venue": "arXiv",
  "versions": []
}