{
  "id": "2103.02012",
  "version": "v1",
  "published": "2021-03-02T20:23:33.000Z",
  "updated": "2021-03-02T20:23:33.000Z",
  "title": "Topological speedups of $\\mathbb{Z}^d$-actions",
  "authors": [
    "Aimee S. A. Johnson",
    "David M. McClendon"
  ],
  "comment": "37 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study minimal $\\mathbb{Z}^d$-Cantor systems and the relationship between their speedups, their collections of invariant Borel measures, their associated unital dimension groups, and their orbit equivalence classes. In the particular case of minimal $\\mathbb{Z}^d$-odometers, we show that their bounded speedups must again be odometers but, contrary to the 1-dimensional case, they need not be conjugate, or even isomorphic, to the original.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-02T20:23:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05"
    ],
    "keywords": [
      "topological speedups",
      "associated unital dimension groups",
      "orbit equivalence classes",
      "invariant borel measures",
      "cantor systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}