{
  "id": "2202.03824",
  "version": "v1",
  "published": "2022-02-08T12:37:35.000Z",
  "updated": "2022-02-08T12:37:35.000Z",
  "title": "On certain elements and the center of the quasi-isometry groups of Euclidean spaces",
  "authors": [
    "Swarup Bhowmik",
    "Prateep Chakraborty"
  ],
  "comment": "13 Pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "We introduce the notion of $PL_\\delta$- homeomorphism between two locally finite simplicial complexes in $\\mathbb{R}^n$ and give a sufficient condition for a simplicial homeomorphism to be a quasi-isometry. We show that the center of the group $QI(\\mathbb{R}^n)$ of all quasi-isometries of $\\mathbb{R}^n$ is trivial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-08T12:37:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "55U10"
    ],
    "keywords": [
      "quasi-isometry groups",
      "euclidean spaces",
      "locally finite simplicial complexes",
      "sufficient condition",
      "simplicial homeomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}