{
  "id": "2308.00266",
  "version": "v1",
  "published": "2023-08-01T04:00:25.000Z",
  "updated": "2023-08-01T04:00:25.000Z",
  "title": "Profinite rigidity and hyperbolic four-punctured sphere bundles over the circle",
  "authors": [
    "Tamunonye Cheetham-West"
  ],
  "comment": "8 pages, 1 figure",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "We show that hyperbolic four-punctured $S^2-$bundles over $S^1$ are distinguished by the finite quotients of their fundamental groups among all 3-manifold groups. To do this, we upgrade a result of Liu to show that the topological type of a fiber is detected by the profinite completion of the fundamental group of a fibered 3-manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-01T04:00:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K32",
      "20E18",
      "57K20"
    ],
    "keywords": [
      "hyperbolic four-punctured sphere bundles",
      "profinite rigidity",
      "fundamental group",
      "finite quotients",
      "profinite completion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}