{
  "id": "1101.1162",
  "version": "v3",
  "published": "2011-01-06T08:20:07.000Z",
  "updated": "2011-10-27T10:26:49.000Z",
  "title": "Three manifold groups, Kaehler groups and complex surfaces",
  "authors": [
    "Indranil Biswas",
    "Mahan Mj",
    "Harish Seshadri"
  ],
  "comment": "v3: 24 pages. This version is slightly different from the version accepted for publication and contains two proofs of finiteness of height of fundamental groups of pieces in the torus decomposition of a 3-manifold. Accepted in Communications in Contemporary Mathematics",
  "journal": "Commun. Contemp. Math. 14, 1250038 (2012) [24 pages]",
  "doi": "10.1142/S0219199712500381",
  "categories": [
    "math.GT",
    "math.AG",
    "math.DG",
    "math.GR"
  ],
  "abstract": "Let $ 1 \\rightarrow N \\rightarrow G \\rightarrow Q \\rightarrow 1$ be an exact sequence of finitely presented groups where Q is infinite and not virtually cyclic, and is the fundamental group of some closed 3-manifold. If G is Kaehler, we show that Q is either the 3-dimensional Heisenberg group or the fundamental group of the Cartesian product of a closed oriented surface of positive genus and the circle. As a corollary, we obtain a new proof of a theorem of Dimca and Suciu by taking N to be the trivial group, If G is the fundamental group of a compact complex surface, we show that Q must be the fundamental group of a Seifert-fibered space and G the fundamental group of an elliptic fibration. We also give an example showing that the relation of quasi-isometry does not preserve Kaehler groups. This gives a negative answer to a question of Gromov which asks whether Kaehler groups can be characterized by their asymptotic geometry.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-10-27T10:26:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "32Q15",
      "57M05",
      "14F35",
      "32J15"
    ],
    "keywords": [
      "fundamental group",
      "manifold groups",
      "compact complex surface",
      "preserve kaehler groups",
      "cartesian product"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.1162B"
    }
  }
}