{
  "id": "1405.2331",
  "version": "v1",
  "published": "2014-05-09T19:55:29.000Z",
  "updated": "2014-05-09T19:55:29.000Z",
  "title": "Fixed points of local actions of nilpotent Lie groups on surfaces",
  "authors": [
    "Morris W. Hirsch"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $G$ be connected nilpotent Lie group acting locally on a real surface $M$. Let $\\varphi$ be the local flow on $M$ induced by a $1$-parameter subgroup. Assume $K$ is a compact set of fixed points of $\\varphi$ and $U$ is a neighborhood of $K$ containing no other fixed points. Theorem: If the Dold fixed-point index of $\\varphi_t|U$ is nonzero for sufficiently small $t>0$, then ${\\rm Fix} (G) \\cap K \\ne \\emptyset$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-09T19:55:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54H15",
      "54H25"
    ],
    "keywords": [
      "fixed points",
      "local actions",
      "lie group acting",
      "dold fixed-point index",
      "local flow"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.2331H"
    }
  }
}