{
  "abstract": "We propose the study of the class of groups that fix a point for every continuous action on any convex compact space. Oliver completed the corresponding program of classifying the finite groups that have this fixed-point property in finite dimensions. Turning to infinite groups, the Schauder--Tychonoff theorem establishes that the integers have the fixed-point property, but this has not been shown for any other infinite, finitely generated group. We establish a local transfer principle and use it to show, as a proof of concept, that $\\mathbf{Z} \\times (\\mathbf{Z}/p\\mathbf{Z})$ belongs to this class of groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18070",
  "author_total": 3,
  "authors": [
    {
      "name": "Nicolas Monod"
    },
    {
      "name": "Omer Tamuz"
    },
    {
      "name": "Lizzy Teryoshin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3n45vf0m64jxz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18070",
  "fulltext_url": null,
  "id": "3n45vf0m64jxz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18070",
  "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.GR"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7221753986",
  "pdf_url": "https://arxiv.org/pdf/2610.18070",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3n45vf0m64jxz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.18070",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18070"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Groups with the fixed-point property",
  "title_text": "Groups with the fixed-point property",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/3n45vf0m64jxz",
  "venue": "arXiv",
  "versions": []
}