{
  "id": "0805.1527",
  "version": "v1",
  "published": "2008-05-11T11:57:01.000Z",
  "updated": "2008-05-11T11:57:01.000Z",
  "title": "Small values of the Lusternik-Schnirelmann category for manifolds",
  "authors": [
    "Alexander N. Dranishnikov",
    "Mikhail G. Katz",
    "Yuli B. Rudyak"
  ],
  "comment": "16 pages, to appear in Geometry and Topology",
  "categories": [
    "math.AT",
    "math.GT"
  ],
  "abstract": "We prove that manifolds of Lusternik-Schnirelmann category 2 necessarily have free fundamental group. We thus settle a 1992 conjecture of Gomez-Larranaga and Gonzalez-Acuna, by generalizing their result in dimension 3, to all higher dimensions. We also obtain some general results on the relations between the fundamental group of a closed manifold M, the dimension of M, and the Lusternik-Schnirelmann category of M, and relate the latter to the systolic category of M.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-11T11:57:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55M30",
      "53C23",
      "57N65"
    ],
    "keywords": [
      "lusternik-schnirelmann category",
      "small values",
      "free fundamental group",
      "general results",
      "higher dimensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.1527D"
    }
  }
}