{
  "id": "2002.01670",
  "version": "v1",
  "published": "2020-02-05T07:39:34.000Z",
  "updated": "2020-02-05T07:39:34.000Z",
  "title": "Special cube complexes revisited: a quasi-median generalisation",
  "authors": [
    "Anthony Genevois"
  ],
  "comment": "31 pages, 5 figures. Comments are welcome!",
  "categories": [
    "math.GR"
  ],
  "abstract": "In this article, we generalise Haglund and Wise's theory of special cube complexes to groups acting on quasi-median graphs. More precisely, we define special actions on quasi-median graphs, and we show that a group which acts specially on a quasi-median graph with finitely many orbits of vertices must embed as a virtual retract into a graph product of finite extensions of clique-stabilisers. In the second part of the article, we apply the theory to fundamental groups of some graphs of groups called right-angled graphs of groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-05T07:39:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20E06"
    ],
    "keywords": [
      "special cube complexes",
      "quasi-median generalisation",
      "quasi-median graph",
      "define special actions",
      "generalise haglund"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}