{
  "abstract": "Let $F$ be a finitely generated free group. We prove that the centraliser of any element of $\\mathrm{Out}(F)$ or $\\mathrm{Aut}(F)$ is of type $\\rm{VF}$. We also prove that the (outer) automorphism group of any free-by-cyclic group $M=F\\rtimes_φ\\mathbb{Z}$ is of type $\\rm{VF}$, and so are the McCool subgroups of $\\mathrm{Out}(M)$. This relies on the construction of a new $\\mathrm{Out}(M)$-invariant splitting of $M$, that enables us to reduce the proof of the above statements to the case where the outer class of $φ$ has finite order.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04581",
  "author_total": 4,
  "authors": [
    {
      "name": "Naomi Andrew"
    },
    {
      "name": "Yassine Guerch"
    },
    {
      "name": "Camille Horbez"
    },
    {
      "name": "Richard D. Wade"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dkc8na0hbd55a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04581",
  "fulltext_url": null,
  "id": "dkc8na0hbd55a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04581",
  "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.GR"
    ],
    [
      "arxiv",
      "math.GT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04581",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dkc8na0hbd55a.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04581",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04581"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Finiteness properties of centralisers in $\\mathrm{Out}(F_N)$ and automorphisms of free-by-cyclic groups",
  "title_text": "Finiteness properties of centralisers in Out(F_N) and automorphisms of free-by-cyclic groups",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:29Z",
  "url": "https://research.draconitic.com/paper/dkc8na0hbd55a",
  "venue": "arXiv",
  "versions": []
}