{
  "id": "1901.02108",
  "version": "v1",
  "published": "2019-01-07T23:59:12.000Z",
  "updated": "2019-01-07T23:59:12.000Z",
  "title": "Geometry of compact lifting spaces",
  "authors": [
    "Gregory R. Conner",
    "Wolfgang Herfort",
    "Petar Pavešić"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "We study a natural generalization of inverse systems of finite regular covering spaces. A limit of such a system is a fibration whose fibres are profinite topological groups. However, as shown in a previous paper (Conner-Herfort-Pavesic: Some anomalous examples of lifting spaces), there are many fibrations whose fibres are profinite groups, which are far from being inverse limits of coverings. We characterize profinite fibrations among a large class of fibrations and relate the profinite topology on the fundamental group of the base with the action of the fundamental group on the fibre, and develop a version of the Borel construction for fibrations whose fibres are profinite groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-07T23:59:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55R05",
      "57M10",
      "54D05"
    ],
    "keywords": [
      "compact lifting spaces",
      "fundamental group",
      "profinite groups",
      "finite regular covering spaces",
      "profinite topological groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}