{
  "id": "1807.09933",
  "version": "v1",
  "published": "2018-07-26T03:08:26.000Z",
  "updated": "2018-07-26T03:08:26.000Z",
  "title": "On the center of the group of quasi-isometries of the real line",
  "authors": [
    "Prateep Chakraborty"
  ],
  "comment": "4 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $QI(\\mathbb{R})$ denote the group of all quasi-isometries $f:\\mathbb{R}\\to \\mathbb{R}.$ Let $Q_+( \\text{and}~ Q_-)$ denote the subgroup of $QI(\\mathbb{R})$ consisting of elements which are identity near $-\\infty$ (resp. $+\\infty$). We denote by $QI^+(\\mathbb R)$ the index $2$ subgroup of $QI(\\mathbb R)$ that fixes the ends $+\\infty, -\\infty$. We show that $QI^+(\\mathbb R)\\cong Q_+\\times Q_-$. Using this we show that the center of the group $QI(\\mathbb{R})$ is trivial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-26T03:08:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F38",
      "20F65"
    ],
    "keywords": [
      "real line",
      "quasi-isometries"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}