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Conjugacy problems in higher-dimensional Thompson groups — arXiv:2610.11124

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.11124
License (as archived): CC0-1.0
Archived: 2026-10-09T06:36:33.754Z
SHA-256 of the archived text: 27df2a7c51daed2c49e3dd392c39e601f90eaf8480ee8509ad82c0ba6eb32887
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How to cite

Conjugacy problems in higher-dimensional Thompson groups — arXiv:2610.11124 — arXiv (en), https://arxiv.org/abs/2610.11124 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_f7bd85b7fa47 (Metraipolis archive dc_f7bd85b7fa47, sha256 27df2a7c51daed2c49e3dd392c39e601f90eaf8480ee8509ad82c0ba6eb32887)

BibTeX

@misc{dcf7bd85b7fa47,
  title = {Conjugacy problems in higher-dimensional Thompson groups — arXiv:2610.11124},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.11124},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_f7bd85b7fa47; sha256 27df2a7c51daed2c49e3dd392c39e601f90eaf8480ee8509ad82c0ba6eb32887},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.11124. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv cs.FL, nuovi lavori del giorno).
Categorie arXiv: Group Theory (math.GR) ; Formal Languages and Automata Theory (cs.FL); Dynamical Systems (math.DS).
Pagina del lavoro: https://arxiv.org/abs/2610.11124 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-09T05:57:46.405Z dalla pagina https://arxiv.org/list/cs.FL/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).