{
  "id": "math/0202120",
  "version": "v1",
  "published": "2002-02-13T09:28:45.000Z",
  "updated": "2002-02-13T09:28:45.000Z",
  "title": "Lusternik-Schnirelmann category of a sphere-bundle over a sphere",
  "authors": [
    "Norio Iwase"
  ],
  "comment": "10 pages",
  "journal": "Topology, 42 (2003), 701--713",
  "categories": [
    "math.AT"
  ],
  "abstract": "A criterion to determine the L-S category of a total space of a sphere-bundle over a sphere is given in terms of homotopy invariants of its characteristic map, and thus providing a complete answer to Ganea's Problem 4. As a result, we obtain a necessary and sufficient condition for such a total space $N$ to have the same L-S category as its `once punctured submanifold' $N\\smallsetminus\\{P\\}$, $P \\in N$. Also a necessary condition for such a total space $M$ to satisfy Ganea's conjecture is obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-02-13T09:28:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55M30",
      "55P35",
      "55Q25",
      "55R35",
      "55S36"
    ],
    "keywords": [
      "lusternik-schnirelmann category",
      "total space",
      "sphere-bundle",
      "l-s category",
      "satisfy ganeas conjecture"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......2120I"
    }
  }
}