{
  "id": "2202.04911",
  "version": "v1",
  "published": "2022-02-10T09:07:43.000Z",
  "updated": "2022-02-10T09:07:43.000Z",
  "title": "The group of quasi-isometries of the real line cannot act effectively on the line",
  "authors": [
    "Shengkui Ye",
    "Yanxin Zhao"
  ],
  "categories": [
    "math.GT",
    "math.DS",
    "math.GR"
  ],
  "abstract": "We prove that the group $\\mathrm{QI}^{+}(\\mathbb{R})$ of orientation-preserving quasi-isometries of the real line is a left-orderable, non-simple group, which cannot act effectively on the real line $\\mathbb{R}.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-10T09:07:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "real line",
      "non-simple group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}