{
  "abstract": "Given a finite rank Coxeter system, we construct a hyperbolic space by coning off the wide parabolic subcomplexes of its Davis complex. The resulting space is ``stability recognizing'', in the sense that stable subspaces of the Davis complex are exactly the quasigeodesically connected subspaces whose images in the coned-off space are quasiisometrically embedded. Equivalently, the coned-off space is ``Morse recognizing'': a quasigeodesic in the Davis complex is Morse if and only if it is quasigeodesic in the coned-off space. Similar results are true for the mapping class group of a hyperbolic surface acting on its curve graph. We strengthen this analogy with additional results. First, the action of the Coxeter group on the coned-off space is acylindrical and gives the largest acylindrically hyperbolic structure for the Coxeter group. Second, the stable subgroups of a Coxeter group are characterized as the finitely generated subgroups that are undistorted and purely loxodromic with respect to the action on the coned-off space. The coned-off space, being constructed directly from the Coxeter structure, facilitates concrete characterizations of Morseness and stability for two important Coxeter-native families of objects: combinatorial geodesics and special subgroups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.17036",
  "author_total": 3,
  "authors": [
    {
      "name": "Christopher H. Cashen"
    },
    {
      "name": "Michelle Chu"
    },
    {
      "name": "Jing Tao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9smsfpk3ehtmj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.17036",
  "fulltext_url": null,
  "id": "9smsfpk3ehtmj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.17036",
  "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",
      "math.GR"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7203782536",
  "pdf_url": "https://arxiv.org/pdf/2608.17036",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9smsfpk3ehtmj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2608.17036",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.17036"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Hyperbolic models and stability recognition for Coxeter groups",
  "title_text": "Hyperbolic models and stability recognition for Coxeter groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/9smsfpk3ehtmj",
  "venue": "arXiv",
  "versions": []
}