{
  "id": "2002.07383",
  "version": "v1",
  "published": "2020-02-18T05:49:20.000Z",
  "updated": "2020-02-18T05:49:20.000Z",
  "title": "Fibrations, and stability of compact group actions on manifolds with local bounded Ricci covering geometry",
  "authors": [
    "Hongzhi Huang"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "In this work, we (partially) generalize two classical tools in study of collapsed manifolds with bounded sectional curvature: a (singular) fibration theorem by Fukaya (1987) and Cheeger-Fukaya-Gromov (1992), and the stability of isometric compact Lie group actions on manifolds by Palais (1961) and Grove-Karcher (1973), to manifolds with local bounded Ricci covering geometry. Our two generalized results have been used in a recent work of Xiaochun Rong in generalizing Gromov's almost flat manifolds theorem to maximally collapsed manifolds with local bounded Ricci covering geometry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-18T05:49:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local bounded ricci covering geometry",
      "compact group actions",
      "compact lie group actions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}