{
  "id": "2309.16791",
  "version": "v1",
  "published": "2023-09-28T18:38:33.000Z",
  "updated": "2023-09-28T18:38:33.000Z",
  "title": "Group rings and hyperbolic geometry",
  "authors": [
    "Grigori Avramidi",
    "Thomas Delzant"
  ],
  "comment": "29 pages",
  "categories": [
    "math.GT",
    "math.GR",
    "math.RA"
  ],
  "abstract": "For a group acting on a hyperbolic space, we set up an algorithm in the group algebra showing that ideals generated by few elements are free, where few is a function of the minimal displacement of the action, and derive algebraic, geometric, and topological consequences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-28T18:38:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperbolic geometry",
      "group rings",
      "hyperbolic space",
      "minimal displacement",
      "group algebra showing"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}