{
  "id": "0910.5207",
  "version": "v2",
  "published": "2009-10-27T18:58:24.000Z",
  "updated": "2010-09-19T23:29:39.000Z",
  "title": "Cohomogeneity One Alexandrov Spaces",
  "authors": [
    "Fernando Galaz-Garcia",
    "Catherine Searle"
  ],
  "comment": "15 pages; Proposition 2.2 in v1 (now Proposition 4) has been modified. An omission in the classification of cohomogeneity one 4-manifolds was corrected",
  "categories": [
    "math.DG",
    "math.MG"
  ],
  "abstract": "We obtain a structure theorem for closed, cohomogeneity one Alexandrov spaces and we classify closed, cohomogeneity one Alexandrov spaces in dimensions 3 and 4. As a corollary, we obtain the classification of closed, $n$-dimensional, cohomogeneity one Alexandrov spaces admitting an isometric $T^{n-1}$ action. In contrast to the 1- and 2-dimensional cases, where it is known that an Alexandrov space is a topological manifold, in dimension 3 the classification contains, in addition to the known cohomogeneity one manifolds, the spherical suspension of $RP^2$, which is not a manifold.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-09-19T23:29:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "57S25",
      "51M25"
    ],
    "keywords": [
      "cohomogeneity",
      "structure theorem",
      "classification contains",
      "alexandrov spaces admitting",
      "topological manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.5207G"
    }
  }
}