{
  "id": "1810.13056",
  "version": "v1",
  "published": "2018-10-31T01:07:33.000Z",
  "updated": "2018-10-31T01:07:33.000Z",
  "title": "Volume pinching theorems for CAT(1) spaces",
  "authors": [
    "Koichi Nagano"
  ],
  "comment": "18 pages",
  "categories": [
    "math.DG",
    "math.MG"
  ],
  "abstract": "We examine volume pinching problems of CAT(1) spaces. We characterize a class of compact geodesically complete CAT(1) spaces of small specific volume. We prove a sphere theorem for compact CAT(1) homology manifolds of small volume. We also formulate a criterion of manifold recognition for homology manifolds on volume growths under an upper curvature bound.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-31T01:07:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "53C23",
      "57P05"
    ],
    "keywords": [
      "volume pinching theorems",
      "homology manifolds",
      "compact geodesically complete cat",
      "small specific volume",
      "upper curvature bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}