{
  "id": "math/9808085",
  "version": "v1",
  "published": "1998-08-18T22:25:30.000Z",
  "updated": "1998-08-18T22:25:30.000Z",
  "title": "On normal subgroups in the fundamental groups of complex surfaces",
  "authors": [
    "Michael Kapovich"
  ],
  "categories": [
    "math.GT",
    "math.AG"
  ],
  "abstract": "We show that for each aspherical compact complex surface $X$ whose fundamental group $\\pi$ fits into a short exact sequence $$ 1\\to K \\to \\pi \\to \\pi_1(S) \\to 1 $$ where $S$ is a compact hyperbolic Riemann surface and the group $K$ is finitely-presentable, there is a complex structure on $S$ and a nonsingular holomorphic fibration $f: X\\to S$ which induces the above short exact sequence. In particular, the fundamental groups of compact complex-hyperbolic surfaces cannot fit into the above short exact sequence. As an application we give the first example of a non-coherent uniform lattice in $PU(2,1)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-08-18T22:25:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fundamental group",
      "short exact sequence",
      "normal subgroups",
      "compact hyperbolic riemann surface",
      "compact complex-hyperbolic surfaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......8085K"
    }
  }
}