{
  "abstract": "We prove that topological conjugacy of elements of the Brin--Thompson group $nV$ is undecidable for every $n\\geq2$. From a Turing machine $T$, the reduction produces two elements of $nV$, which are conjugate by an involution in $nV$ if $T$ halts on the empty tape. If $T$ does not halt on the empty tape, the topological dynamics of the two group elements are distinguished by their visits to minimal subsystems of the set of (germ-)aperiodic points. In these groups, and any finitely-generated supergroups inside the homeomorphism group of Cantor space, we also obtain undecidability of the Whitehead problem (the problem of being in the same automorphism orbit), and undecidability of group-theoretic conjugacy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11124",
  "author_total": 1,
  "authors": [
    {
      "name": "Ville Salo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/151pwcjyv93gw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11124",
  "fulltext_url": null,
  "id": "151pwcjyv93gw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11124",
  "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",
      "cs.FL"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7221106947",
  "pdf_url": "https://arxiv.org/pdf/2610.11124",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/151pwcjyv93gw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11124",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11124"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Conjugacy problems in higher-dimensional Thompson groups",
  "title_text": "Conjugacy problems in higher-dimensional Thompson groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/151pwcjyv93gw",
  "venue": "arXiv",
  "versions": []
}