{
  "id": "1303.1058",
  "version": "v3",
  "published": "2013-03-05T15:05:48.000Z",
  "updated": "2014-10-16T14:57:58.000Z",
  "title": "Higgs bundles for the non-compact dual of the special orthogonal group",
  "authors": [
    "Steven B. Bradlow",
    "Oscar Garcia-Prada",
    "Peter B. Gothen"
  ],
  "comment": "43 pages; v2: minor corrections and improvements, appendix significantly shortened (the removed material will appear elsewhere); v3: final version with many minor corrections and improvements, to appear in Geometriae Dedicata",
  "categories": [
    "math.AG",
    "math.DG"
  ],
  "abstract": "Higgs bundles over a closed orientable surface can be defined for any real reductive Lie group G. In this paper we examine the case G=SO*(2n). We describe a rigidity phenomenon encountered in the case of maximal Toledo invariant. Using this and Morse theory in the moduli space of Higgs bundles, we show that the moduli space is connected in this maximal Toledo case. The Morse theory also allows us to show connectedness when the Toledo invariant is zero. The correspondence between Higgs bundles and surface group representations thus allows us to count the connected components with zero and maximal Toledo invariant in the moduli space of representations of the fundamental group of the surface in SO*(2n).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-07-18T20:13:21.000Z",
      "comment": "43 pages; v2: minor corrections and improvements, appendix significantly shortened (the removed material will appear elsewhere)",
      "journal": null,
      "doi": "10.1112/jtopol/jts030"
    },
    {
      "version": "v3",
      "updated": "2014-10-16T14:57:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H60",
      "53C07",
      "58D29"
    ],
    "keywords": [
      "higgs bundles",
      "special orthogonal group",
      "non-compact dual",
      "moduli space",
      "maximal toledo invariant"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.1058B"
    }
  }
}