{
  "id": "1402.1612",
  "version": "v1",
  "published": "2014-02-07T12:08:21.000Z",
  "updated": "2014-02-07T12:08:21.000Z",
  "title": "On Jordan type bounds for finite groups of diffeomorphisms of 3-manifolds and Euclidean spaces",
  "authors": [
    "Bruno P. Zimmermann"
  ],
  "comment": "seven pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "By a classical result of Jordan, each finite subgroup G of a complex linear group GL_n(C) has an abelian subgroup whose index in G is bounded by a constant depending only on n. We consider the problem if this remains true for finite subgroups G of the diffeomorphism group of a smooth manifold, and show that it is true for all compact 3-manifolds as well as for Euclidean spaces of dimension n < 7. The question remains open at present e.g. for odd-dimensional spheres of dimension greater or equal to five, and for Euclidean spaces of dimension greater or equal to seven.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-07T12:08:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "euclidean spaces",
      "jordan type bounds",
      "finite groups",
      "dimension greater",
      "finite subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.1612Z"
    }
  }
}