{
  "id": "0810.5533",
  "version": "v3",
  "published": "2008-10-30T19:55:32.000Z",
  "updated": "2009-07-29T13:39:27.000Z",
  "title": "Characterization of Line Arrangement for which the Fundamental Group of the Complement is a Direct Product of Free Groups",
  "authors": [
    "Eliyahu Meital",
    "Liberman Eran",
    "Schaps Mary",
    "Teicher Mina"
  ],
  "comment": "16 pages",
  "categories": [
    "math.AT",
    "math.GR",
    "math.GT"
  ],
  "abstract": "Kwai Man Fan proved that if the intersection lattice of a line arrangement does not contain a cycle, then the fundamental group of its complement is a direct sum of infinite and cyclic free groups. He also conjectured that the converse is true as well. The main purpose of this paper is to prove this conjecture",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-07-29T13:39:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32S22",
      "14N30",
      "52C30"
    ],
    "keywords": [
      "fundamental group",
      "line arrangement",
      "direct product",
      "complement",
      "characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.5533M"
    }
  }
}