{
  "id": "1601.02992",
  "version": "v1",
  "published": "2016-01-12T18:36:13.000Z",
  "updated": "2016-01-12T18:36:13.000Z",
  "title": "Zero sets of Abelian Lie algebras of vector fields",
  "authors": [
    "Morris W. Hirsch"
  ],
  "comment": "8 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Assume M is a 3-dimensional real manifold without boundary, A is an abelian Lie algebra of analytic vector fields on M, and X is an element of A. The following result is proved: If K is a locally maximal compact set of zeroes of X and the Poincar'e-Hopf index of X at K is nonzero, there is a point in K at which all the elements of A vanish.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-12T18:36:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B66",
      "37B30",
      "58K45"
    ],
    "keywords": [
      "abelian lie algebra",
      "zero sets",
      "analytic vector fields",
      "locally maximal compact set",
      "poincare-hopf index"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}