{
  "id": "math/0009203",
  "version": "v2",
  "published": "2000-09-22T14:10:24.000Z",
  "updated": "2001-08-27T19:59:17.000Z",
  "title": "The Moduli of Flat PU(p,p)-Structures with Large Toledo Invariants",
  "authors": [
    "Eyal Markman",
    "Eugene Z. Xia"
  ],
  "comment": "16 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "For a compact Riemann surface $X$ of genus $g > 1$, $\\Hom(\\pi_1(X), PU(p,q))/PU(p,q)$ is the moduli space of flat $PU(p,q)$-connections on $X$. There are two invariants, the Chern class $c$ and the Toledo invariant $\\tau$ associated with each element in the moduli. The Toledo invariant is bounded in the range $-2min(p,q)(g-1) \\le \\tau \\le 2min(p,q)(g-1)$. This paper shows that the component, associated with a fixed $\\tau > 2(max(p,q)-1)(g-1)$ (resp. $\\tau < -2(max(p,q)-1)(g-1)$) and a fixed Chern class $c$, is connected (The restriction on $\\tau$ implies $p=q$).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2001-08-27T19:59:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D20",
      "14H60"
    ],
    "keywords": [
      "large toledo invariants",
      "flat pu",
      "compact riemann surface",
      "chern class",
      "moduli space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......9203M"
    }
  }
}