{
  "id": "math/0507491",
  "version": "v1",
  "published": "2005-07-23T05:16:41.000Z",
  "updated": "2005-07-23T05:16:41.000Z",
  "title": "Lusternik-Schnirelmann category of Spin{9}",
  "authors": [
    "Norio Iwase",
    "Akira Kono"
  ],
  "comment": "12pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "Let G be a compact connected Lie group and p : E \\to {\\Sigma}^2V a principal G-bundle with a characteristic map \\alpha : A={\\Sigma}V \\to G. By combining cone decomposition arguments in Iwase-Mimura-Nishimoto [3,5] with computations of higher Hopf invariants introduced in Iwase [8], we generalize the result in Iwase-Mimura [12]: Let {F_{i}|0 \\leq i \\leq m} be a cone-decomposition of G with a canonical structure map \\sigma_{i} of cat(F_{i}) \\leq i for i \\leq m. We have cat(E) \\leq \\Max(m+n,m+2) for n \\geq 1, if \\alpha is compressible into F_{n} \\subseteq F_{m} \\simeq G and H^{\\sigma_n}_n(\\alpha) = 0, under a suitable compatibility condition. On the other hand, calculations of Hamanaka-Kono [3] and Ishitoya-Kono-Toda [5] on spinor groups yields a lower estimate for the L-S category of spinor groups by means of a new computable invariant Mwgt(-;{mathbb{F}_2}) which is stronger than wgt(-;{\\mathbb{F}_2}) introduced in Rudyak [16] and Strom [18]. As a result, we obtain cat(Spin(9)) = Mwgt(Spin(9);\\mathbb{F}_2) = 8 > 6 = wgt(Spin(9);\\mathbb{F}_2).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-07-23T05:16:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55M30",
      "55N20",
      "57T30"
    ],
    "keywords": [
      "lusternik-schnirelmann category",
      "spinor groups yields",
      "compact connected lie group",
      "higher hopf invariants",
      "combining cone decomposition arguments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7491I"
    }
  }
}