{
  "id": "1607.00445",
  "version": "v1",
  "published": "2016-07-02T01:29:54.000Z",
  "updated": "2016-07-02T01:29:54.000Z",
  "title": "Extension properties of asymptotic property C and finite decomposition complexity",
  "authors": [
    "Susan Beckhardt",
    "Boris Goldfarb"
  ],
  "comment": "10 pages",
  "categories": [
    "math.GT",
    "math.GR",
    "math.MG"
  ],
  "abstract": "We prove extension theorems for several geometric properties such as asymptotic property C (APC), finite decomposition complexity (FDC), strict finite decomposition complexity (sFDC) which are weakenings of Gromov's finite asymptotic dimension (FAD). The context of all theorems is a finitely generated group $G$ with a word metric and a coarse quasi-action on a metric space $X$. We assume that the quasi-stabilizers have a property $P_1$, and $X$ has the same or sometimes a weaker property $P_2$. Then $G$ also has property $P_2$. We show some sample applications, discuss constraints to further generalizations, and illustrate the flexibility that the weak quasi-action assumption allows.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-02T01:29:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic property",
      "extension properties",
      "strict finite decomposition complexity",
      "gromovs finite asymptotic dimension",
      "weak quasi-action assumption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}