{
  "id": "2309.08328",
  "version": "v1",
  "published": "2023-09-15T11:34:38.000Z",
  "updated": "2023-09-15T11:34:38.000Z",
  "title": "Topological Rigidity of the Dynamic Asymptotic Dimension",
  "authors": [
    "Samantha Pilgrim"
  ],
  "comment": "9 pages, comments welcome",
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that when $X$ is compact and totally disconnected or a finite union of compact manifolds (possibly with boundary), that the dynamic asymptotic dimension of a free action of a countable group $\\Gamma$ on $X$ by homeomorphisms is either infinite or the asymptotic dimension of $\\Gamma$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-15T11:34:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B99",
      "46L35"
    ],
    "keywords": [
      "dynamic asymptotic dimension",
      "topological rigidity",
      "finite union",
      "free action",
      "compact manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}