{
  "id": "1208.4510",
  "version": "v4",
  "published": "2012-08-22T14:32:44.000Z",
  "updated": "2014-05-06T16:52:46.000Z",
  "title": "Fixed points of nilpotent actions on ${\\mathbb S}^{2}$",
  "authors": [
    "Javier Ribón"
  ],
  "comment": "Some clarifications and minor corrections added",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that a nilpotent subgroup of orientation preserving $C^{1}$ diffeomorphisms of ${\\mathbb S}^{2}$ has a finite orbit of cardinality at most two. We also prove that a finitely generated nilpotent subgroup of orientation preserving $C^{1}$ diffeomorphisms of ${\\mathbb R}^{2}$ preserving a compact set has a global fixed point. These results generalize theorems of Franks, Handel and Parwani for the abelian case. We show that a nilpotent subgroup of orientation preserving $C^{1}$ diffeomorphisms of ${\\mathbb S}^{2}$ that has a finite orbit of odd cardinality also has a global fixed point. Moreover we study the properties of the two-points orbits of nilpotent fixed-point-free subgroups of orientation preserving $C^{1}$ diffeomorphisms of ${\\mathbb S}^{2}$.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-05-06T16:52:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E30",
      "37C85"
    ],
    "keywords": [
      "nilpotent actions",
      "orientation preserving",
      "global fixed point",
      "diffeomorphisms",
      "finite orbit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.4510R"
    }
  }
}