{
  "id": "1508.04503",
  "version": "v1",
  "published": "2015-08-19T02:30:40.000Z",
  "updated": "2015-08-19T02:30:40.000Z",
  "title": "Vanishing theorems on foliations",
  "authors": [
    "Weiping Zhang"
  ],
  "comment": "15 pages. arXiv admin note: text overlap with arXiv:1204.2224",
  "categories": [
    "math.DG",
    "math.GT"
  ],
  "abstract": "We prove the following generalization of the Lichnerowicz-Hitchin vanishing theorem to the case of foliations: let $M$ be a closed spin manfold, let $F$ be an integrable subbundle of the tangent bundle $TM$ such that $F$ carries a metric of positive leafwise scalar curvature, then the canonical $KO$-characteristic number $\\hat{\\mathcal A}(M)$ vanishes. Our proof applies to give a geometric proof of the Connes vanishing theorem, which states that in the case of $F$ being spin instead of $TM$ being spin, one has $\\hat{A}(M)=0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-19T02:30:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "foliations",
      "tangent bundle",
      "lichnerowicz-hitchin vanishing theorem",
      "positive leafwise scalar curvature",
      "closed spin manfold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150804503Z"
    }
  }
}