{
  "id": "2012.13368",
  "version": "v1",
  "published": "2020-12-24T17:51:51.000Z",
  "updated": "2020-12-24T17:51:51.000Z",
  "title": "The first $\\ell^2$-Betti number and groups acting on trees",
  "authors": [
    "Indira Chatterji",
    "Sam Hughes",
    "Peter Kropholler"
  ],
  "comment": "6 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "We generalise results of Thomas, Allcock, Thom-Petersen, and Kar-Niblo to the first $\\ell^2$-Betti number of quotients of certain groups acting on trees by subgroups with free actions on the edge sets of the graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-24T17:51:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20J05",
      "20E08",
      "20F05"
    ],
    "keywords": [
      "betti number",
      "groups acting",
      "generalise results",
      "free actions",
      "edge sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}