{
  "abstract": "We prove Mühlherr's Twist Conjecture: any two angle-compatible Coxeter generating sets of a Coxeter group differ by a finite sequence of elementary twists and a conjugation. Combined with earlier work of Howlett-Mühlherr and Marquis-Mühlherr, this completes the resolution of the Isomorphism Problem for Coxeter groups. A further consequence is that ${\\rm Aut}(W)$ is finitely generated for every Coxeter group $W$, and there is an algorithm producing a finite set of generators for ${\\rm Aut}(W)$ starting from any Coxeter matrix. Of the vast literature on the Twist Conjecture, we utilise only two results in an essential way: strong rigidity of $2$--spherical Coxeter systems, due to Caprace and Mühlherr, and the framework of markings and hierarchies developed by Caprace and Przytycki for the twist-rigid case. We also exploit in a fundamental way some soft ideas from JSJ theory and an observation of Mihalik-Tschantz on splittings of Coxeter groups. No form of AI was used in the writing of this manuscript, nor in the research that it presents.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28348",
  "author_total": 1,
  "authors": [
    {
      "name": "Elia Fioravanti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/axnanwqynvv5s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28348",
  "fulltext_url": null,
  "id": "axnanwqynvv5s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28348",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
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  "openalex": "W7204850902",
  "pdf_url": "https://arxiv.org/pdf/2608.28348",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/axnanwqynvv5s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.28348",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28348"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The Twist Conjecture and the Isomorphism Problem for Coxeter groups",
  "title_text": "The Twist Conjecture and the Isomorphism Problem for Coxeter groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/axnanwqynvv5s",
  "venue": "arXiv",
  "versions": []
}