{
  "id": "1912.11502",
  "version": "v1",
  "published": "2019-12-24T19:39:38.000Z",
  "updated": "2019-12-24T19:39:38.000Z",
  "title": "A self-contained account of why Thompson's group $F$ is of type $\\textrm{F}_\\infty$",
  "authors": [
    "Matthew C. B. Zaremsky"
  ],
  "comment": "7 pages, 3 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "In 1984 Brown and Geoghegan proved that Thompson's group $F$ is of type $\\textrm{F}_\\infty$, making it the first example of an infinite dimensional torsion-free group of type $\\textrm{F}_\\infty$. Over the decades a different, shorter proof has emerged, which is more streamlined and generalizable to other groups. It is difficult, however, to isolate this proof in the literature just for $F$ itself, with no complicated generalizations considered and no additional properties proved. The goal of this expository note then is to present the \"modern\" proof that $F$ is of type $\\textrm{F}_\\infty$, and nothing else.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-24T19:39:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "thompsons group",
      "self-contained account",
      "infinite dimensional torsion-free group",
      "shorter proof",
      "first example"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}