{
  "id": "1809.06183",
  "version": "v1",
  "published": "2018-09-17T13:17:40.000Z",
  "updated": "2018-09-17T13:17:40.000Z",
  "title": "Topological regularity of spaces with an upper curvature bound",
  "authors": [
    "Alexander Lytchak",
    "Koichi Nagano"
  ],
  "categories": [
    "math.DG",
    "math.MG"
  ],
  "abstract": "We prove that a locally compact space with an upper curvature bound is a topological manifold if and only if all of its spaces of directions are homotopy equivalent and not contractible. We discuss applications to homology manifolds, limits of Riemannian manifolds and deduce a sphere theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-17T13:17:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "53C23",
      "57P05"
    ],
    "keywords": [
      "upper curvature bound",
      "topological regularity",
      "locally compact space",
      "homotopy equivalent",
      "homology manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}