{
  "abstract": "Let $\\Gamma$ be a Coxeter graph, and let $S$ be its vertex set. An elemental complex over $\\Gamma$ is an abstract simplicial complex $\\mathcal D$ on $S$ that contains every pair $\\{s, t\\}$ with $s \\neq t$ and $m_{s,t} \\neq \\infty$. To each elemental complex $\\mathcal D$, we associate a cube complex $\\Xi_{\\mathcal D}$ on which the virtual Artin group ${\\rm VA} [\\Gamma]$ acts. We prove that $\\Xi_{\\mathcal D}$ is connected, simply connected, and locally regular; that the action of ${\\rm VA}[\\Gamma]$ on $\\Xi_{\\mathcal D}$ is regular, cocompact, and by isometries; and that the stabilizers of cells are parabolic subgroups. We finally prove that $\\Xi_{\\mathcal D}$ is CAT(0) if and only if ${\\mathcal D}$ is a flag complex.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.24840",
  "author_total": 2,
  "authors": [
    {
      "name": "José Galvez Mateos"
    },
    {
      "name": "Luis Paris"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ag9b13x94wb8t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.24840",
  "fulltext_url": null,
  "id": "ag9b13x94wb8t",
  "issns": [],
  "landing_url": "https://hal.science/hal-05703062v3",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-gr"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7171702935",
  "pdf_url": "https://hal.science/hal-05703062/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ag9b13x94wb8t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:03Z",
      "native_id": "hal-05703062",
      "source": "hal",
      "url": "https://hal.science/hal-05703062v3"
    },
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2607.24840",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.24840"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A cube complex for virtual Artin groups",
  "title_text": "A cube complex for virtual Artin groups",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:51Z",
  "url": "https://research.draconitic.com/paper/ag9b13x94wb8t",
  "venue": "HAL",
  "versions": []
}