{
  "abstract": "We prove that the braided Thompson groups $BV$ and $BF$ are Hopfian, answering the two parts of Zaremsky's question. We also prove that, for every discrete group $G$, the labeled Thompson group $V(G)$ is Hopfian if and only if $G$ is Hopfian, proving a conjecture of Wu--Wu--Zhao--Zhou. The second result allows us to prove a new embedding result for Hopfian groups: every Hopfian group of type $F_n$ embeds quasi-isometrically as a subgroup of a Hopfian, boundedly acyclic, acyclic group of type $F_n$ that has no proper finite-index subgroups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.42050",
  "author_total": 1,
  "authors": [
    {
      "name": "Mengfei Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1r7wrwhsnfj3f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.42050",
  "fulltext_url": null,
  "id": "1r7wrwhsnfj3f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.42050",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.42050",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1r7wrwhsnfj3f.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.42050",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.42050"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Hopficity of braided and labeled Thompson groups",
  "title_text": "Hopficity of braided and labeled Thompson groups",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/1r7wrwhsnfj3f",
  "venue": "arXiv",
  "versions": []
}