{
  "id": "math/0003094",
  "version": "v2",
  "published": "2000-03-16T21:25:41.000Z",
  "updated": "2002-07-09T19:44:59.000Z",
  "title": "Relations in the cohomology ring of the moduli space of rank 2 Higgs bundles",
  "authors": [
    "Tamas Hausel",
    "Michael Thaddeus"
  ],
  "comment": "31 pages, LaTeX. Changes in title and introduction only",
  "categories": [
    "math.AG",
    "math-ph",
    "math.DG",
    "math.MP",
    "math.SG"
  ],
  "abstract": "The moduli space of stable bundles of rank 2 and degree 1 on a Riemann surface has rational cohomology generated by the so-called universal classes. The work of Baranovsky, King-Newstead, Siebert-Tian and Zagier provided a complete set of relations between these classes, expressed in terms of a recursion in the genus. This paper accomplishes the same thing for the non-compact moduli spaces of Higgs bundles, in the sense of Hitchin and Simpson. There are many more independent relations than for stable bundles, but in a sense the answer is simpler, since the formulas are completely explicit, not recursive. The results of Kirwan on equivariant cohomology for holomorphic circle actions are of key importance. Together, Parts I and II describe the cohomology rings of spaces of rank 2 Higgs bundles at essentially the same level of detail as is known for stable bundles.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-07-09T19:44:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H60",
      "14D20",
      "14H81",
      "32Q55",
      "58D27"
    ],
    "keywords": [
      "higgs bundles",
      "cohomology ring",
      "stable bundles",
      "non-compact moduli spaces",
      "holomorphic circle actions"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......3094H"
    }
  }
}