{
  "id": "math/0503734",
  "version": "v1",
  "published": "2005-03-31T12:53:44.000Z",
  "updated": "2005-03-31T12:53:44.000Z",
  "title": "Stabilizers and orbits of circle-valued smooth functions",
  "authors": [
    "Sergey Maksymenko"
  ],
  "comment": "11 pages, 1 figure. This paper is an extension of author's preprint http://xxx.lanl.gov/math.FA/0411612 to circle-valued functions",
  "categories": [
    "math.FA",
    "math.AT",
    "math.DS",
    "math.GT"
  ],
  "abstract": "Let $M$ be a smooth compact manifold and $P$ be either $R^1$ or $S^1$. There is a natural action of the groups $Diff(M)$ and $Diff(M) \\times Diff(P)$ on the space of smooth mappings $C^{\\infty}(M,P)$. For $f\\in C^{\\infty}(M,P)$ let $S_f$, $S_{MP}$, $O_f$, and $O_{MP}$ be the stabilizers and orbits of $f$ under these actions. Recently, the author proved that under mild conditions on $f\\in C^{\\infty}(M,R^1)$ the corresponding stabilizers and orbits are homotopy equivalent: $S_{MR} \\sim S_{M}$ and $O_{MR} \\sim O_M$. These results are extended here to the actions on $C^{\\infty}(M,S^1)$. It is proved that under the similar conditions (that are rather typical) we have that $S_{MS}\\sim S_M$ and $O_{MS} \\sim O_M \\times S^1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-03-31T12:53:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58K05",
      "14H40"
    ],
    "keywords": [
      "circle-valued smooth functions",
      "smooth compact manifold",
      "similar conditions",
      "homotopy equivalent",
      "natural action"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3734M"
    }
  }
}