{
  "id": "math/0110087",
  "version": "v1",
  "published": "2001-10-08T18:26:34.000Z",
  "updated": "2001-10-08T18:26:34.000Z",
  "title": "Restrictions on collapsing with a lower sectional curvature bound",
  "authors": [
    "Vitali Kapovitch"
  ],
  "categories": [
    "math.DG",
    "math.MG"
  ],
  "abstract": "We obtain new topological information about the local structure of collapsing under a lower sectional curvature bound. As an application we prove a new sphere theorem and obtain a partial result towards the conjecture that not every Alexandrov space can be obtained as a limit of a sequence of Riemannian manifolds with sectional curvature bounded from below.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-10-08T18:26:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20"
    ],
    "keywords": [
      "lower sectional curvature bound",
      "restrictions",
      "collapsing",
      "local structure",
      "sphere theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....10087K"
    }
  }
}