{
  "id": "1404.5374",
  "version": "v2",
  "published": "2014-04-22T03:52:52.000Z",
  "updated": "2014-04-24T08:32:37.000Z",
  "title": "Actions of groups of diffeomorphisms on one-manifolds by $C^1$ diffeomorphisms",
  "authors": [
    "Shigenori Matsumoto"
  ],
  "comment": "8 pages. arXiv admin note: text overlap with arXiv:1308.5381",
  "categories": [
    "math.DS"
  ],
  "abstract": "Denote by $\\DC(M)_0$ the identity component of the group of the compactly supported $C^r$ diffeomorphisms of a connected $C^\\infty$ manifold $M$. We show that if $\\dim(M)\\geq2$ and $r\\neq \\dim(M)+1$, then any homomorphism from $\\DC(M)_0$ to ${\\Diff}^1(\\R)$ or ${\\Diff}^1(S^1)$ is trivial.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-24T08:32:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57S05",
      "22F05"
    ],
    "keywords": [
      "diffeomorphisms",
      "one-manifolds",
      "identity component"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.5374M"
    }
  }
}