{
  "abstract": "In this paper, we investigate the realizability problem, which asks whether prescribed group actions on graded modules can be realized by the groups of self-homotopy equivalences of CW-complexes acting on their homology. We provide a partial answer in the case of arbitrary groups and permutation modules concentrated in certain degrees. As a consequence, we realize every group as the group of self-homotopy equivalences of an $R$-local CW-complex with arbitrary prescribed connectivity, where $R$ may be chosen with $ρ(R)$ sufficiently large. In particular, this provides a complete answer to Kahn's realizability problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04516",
  "author_total": 3,
  "authors": [
    {
      "name": "Yang Bai"
    },
    {
      "name": "Chaoshun Yang"
    },
    {
      "name": "Xiugui Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/erm23z8029zqr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04516",
  "fulltext_url": null,
  "id": "erm23z8029zqr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04516",
  "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"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7220674838",
  "pdf_url": "https://arxiv.org/pdf/2610.04516",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/erm23z8029zqr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.04516",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04516"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Realization of permutation modules as homology of CW-complexes",
  "title_text": "Realization of permutation modules as homology of CW-complexes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/erm23z8029zqr",
  "venue": "arXiv",
  "versions": []
}