{
  "id": "1206.0263",
  "version": "v2",
  "published": "2012-06-01T17:50:21.000Z",
  "updated": "2020-01-09T21:14:39.000Z",
  "title": "Some topological properties of surface bundles",
  "authors": [
    "Ursula Hamenstaedt"
  ],
  "comment": "Due to a gap in the argument in the last section, this part has been removed. The first sections were rewritten and the results expanded, and the article was split into two parts. This is the first part. 13 pages",
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "This note discusses some properties of surface bundles over surfaces which follow from the Milnor Wood inequality for the Euler class of flat circle bundles over surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-01T17:50:21.000Z",
      "title": "Signatures of surface bundles and Milnor Wood inequalities",
      "abstract": "Let E be a surface bundle over a surface. We use a variant of the Milnor Wood inequality to show that $|3\\sigma(E)|\\leq \\chi(E)$.",
      "comment": "20 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2020-01-09T21:14:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R22",
      "57R20"
    ],
    "keywords": [
      "milnor wood inequality",
      "surface bundle",
      "signatures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.0263H"
    }
  }
}