{
  "id": "2008.12572",
  "version": "v1",
  "published": "2020-08-28T10:30:59.000Z",
  "updated": "2020-08-28T10:30:59.000Z",
  "title": "A Markovian and Roe-algebraic approach to asymptotic expansion in measure",
  "authors": [
    "Kang Li",
    "Federico Vigolo",
    "Jiawen Zhang"
  ],
  "categories": [
    "math.DS",
    "math.OA"
  ],
  "abstract": "In this paper, we conduct further studies on geometric and analytic properties of asymptotic expansion in measure. More precisely, we develop a machinery of Markov expansion and obtain an associated structure theorem for asymptotically expanding actions. Based on this, we establish an analytic characterisation for asymptotic expansion in terms of the Dru\\c{t}u-Nowak projection and the Roe algebra of the associated warped cones. As an application, we provide new counterexamples to the coarse Baum-Connes conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-28T10:30:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A30",
      "37A15",
      "46H35",
      "19K56"
    ],
    "keywords": [
      "asymptotic expansion",
      "roe-algebraic approach",
      "coarse baum-connes conjecture",
      "associated structure theorem",
      "analytic characterisation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}