{
  "id": "1603.07639",
  "version": "v1",
  "published": "2016-03-24T16:23:44.000Z",
  "updated": "2016-03-24T16:23:44.000Z",
  "title": "Surface bundles with genus $2$ fibre are not negatively curved",
  "authors": [
    "Caterina Campagnolo"
  ],
  "comment": "10 pages, 1 figure",
  "categories": [
    "math.GT"
  ],
  "abstract": "In the present note we prove that the total space of a $\\Sigma_2$-bundle over a hyperbolic surface does not admit a negatively curved structure. This is a first step towards an answer to the question whether the total space of a surface bundle over a surface admits a hyperbolic structure. The proof relies on the result of Gromov that a word hyperbolic group does not contain a subgroup isomorphic to $\\mathbb{Z}^2$, and on a geometric description of the second homology group of the total space of the bundle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-24T16:23:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50"
    ],
    "keywords": [
      "surface bundle",
      "total space",
      "word hyperbolic group",
      "second homology group",
      "geometric description"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160307639C"
    }
  }
}