{
  "id": "math/0109183",
  "version": "v3",
  "published": "2001-09-24T05:59:06.000Z",
  "updated": "2009-11-12T07:46:37.000Z",
  "title": "Homotopy types of Diffeomorphism groups of noncompact 2-manifolds",
  "authors": [
    "Tatsuhiko Yagasaki"
  ],
  "comment": "27 pages, Definition 3.1 is corrected",
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "Suppose M is a noncompact connected smooth 2-manifold without boundary and let D(M)_0 denote the identity component of the diffeomorphism group of M with the compact-open C^infty-topology. In this paper we investigate the topological type of D(M)_0 and show that D(M)_0 is a topological ell_2-manifold and it has the homotopy type of the circle if M is the plane, the open annulus or the open M\"obius band, and it is contractible in all other cases. When M admits a volume form w, we also discuss the topological type of the group of w-preserving diffeomorphisms of M. To obtain these results we study some fundamental properties of transformation groups on noncompact spaces endowed with weak topology.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-11-12T07:46:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57S05",
      "58D05",
      "57N20",
      "58A10"
    ],
    "keywords": [
      "diffeomorphism group",
      "homotopy type",
      "topological type",
      "volume form",
      "obius band"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......9183Y"
    }
  }
}