{
  "id": "1708.06379",
  "version": "v1",
  "published": "2017-08-21T18:53:42.000Z",
  "updated": "2017-08-21T18:53:42.000Z",
  "title": "Global fixed points for nilpotent actions on the torus",
  "authors": [
    "Sebastião Firmo",
    "Javier Ribón"
  ],
  "comment": "30 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "An isotopic to the identity map of the $2$-torus, that has zero rotation vector with respect to an invariant ergodic probability measure, has a fixed point by a theorem of Franks. We give a version of this result for nilpotent subgroups of isotopic to the identity diffeomorphisms of the $2$-torus. In such a context we guarantee the existence of global fixed points for nilpotent groups of irrotational diffeomorphisms. In particular we show that the derived group of a nilpotent group of isotopic to the identity diffeomorphisms of the $2$-torus has a global fixed point.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-21T18:53:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global fixed point",
      "nilpotent actions",
      "nilpotent group",
      "identity diffeomorphisms",
      "invariant ergodic probability measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}