{
  "id": "1209.1507",
  "version": "v1",
  "published": "2012-09-07T11:58:50.000Z",
  "updated": "2012-09-07T11:58:50.000Z",
  "title": "Note on the Characteristic rank of Vector bundles",
  "authors": [
    "Aniruddha C. Naolekar",
    "Ajay Singh Thakur"
  ],
  "comment": "15 pages, To appear in Math. Slovaca",
  "categories": [
    "math.AT"
  ],
  "abstract": "We define the notion of characteristic rank, $\\mathrm{charrank}_X(\\xi)$, of a real vector bundle $\\xi$ over a connected finite $CW$-complex $X$. This is a bundle-dependent version of the notion of characteristic rank introduced by J\\'{u}lius Korba\\v{s} in 2010. We obtain bounds for the cup length of manifolds in terms of the characteristic rank of vector bundles generalizing a theorem of Korba\\v{s} and compute the characteristic rank of vector bundles over the Dold manifolds, the Moore spaces and the stunted projective spaces amongst others.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-07T11:58:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R20"
    ],
    "keywords": [
      "characteristic rank",
      "real vector bundle",
      "bundle-dependent version",
      "dold manifolds",
      "cup length"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.1507N"
    }
  }
}