{
  "id": "2106.14931",
  "version": "v1",
  "published": "2021-06-28T18:24:17.000Z",
  "updated": "2021-06-28T18:24:17.000Z",
  "title": "Random groups at density $d<3/14$ act non-trivially on a CAT(0) cube complex",
  "authors": [
    "MurphyKate Montee"
  ],
  "comment": "29 pages, 17 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "For random groups in the Gromov density model at $d<3/14$, we construct walls in the Cayley complex $X$ which give rise to a non-trivial action by isometries on a CAT(0) cube complex. This extends results of Ollivier-Wise and Mackay-Przytycki at densities $d<1/5$ and $d<5/24$, respectively. We are able to overcome one of the main combinatorial challenges remaining from the work of Mackay-Przytycki, and we give a construction that plausibly works at any density $d<1/4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-28T18:24:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F67"
    ],
    "keywords": [
      "cube complex",
      "random groups",
      "gromov density model",
      "cayley complex",
      "non-trivial action"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}