{
  "id": "1511.07751",
  "version": "v1",
  "published": "2015-11-24T15:25:36.000Z",
  "updated": "2015-11-24T15:25:36.000Z",
  "title": "Higgs bundles, Toledo invariant and the Cayley correspondence",
  "authors": [
    "Olivier Biquard",
    "Oscar Garcia-Prada",
    "Roberto Rubio"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "We define the Toledo invariant of a G-Higgs bundles on a Riemann surface, where G is a real semisimple group of Hermitian type, and we prove a Milnor-Wood type bound for this invariant when the bundle is semistable. We prove rigidity results when the Toledo invariant is maximal, establishing in particular a Cayley correspondence when the symmetric space defined by G is of tube type. This gives a new proof of the Milnor-Wood inequality of Burger-Iozzi-Wienhard for representations of the fundamental group of a Riemann surface into G. Compared to previous results using Higgs bundles, it uses general theory and avoids any case by case study.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-24T15:25:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H60",
      "57R57",
      "58D29"
    ],
    "keywords": [
      "toledo invariant",
      "higgs bundles",
      "cayley correspondence",
      "riemann surface",
      "real semisimple group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151107751B"
    }
  }
}