{
  "id": "math/0404459",
  "version": "v2",
  "published": "2004-04-26T13:30:21.000Z",
  "updated": "2009-03-23T11:12:22.000Z",
  "title": "The Coxeter quotient of the fundamental group of a Galois cover of T \\times T",
  "authors": [
    "Amram Meirav",
    "Mina Teicher",
    "Uzi Vishne"
  ],
  "comment": "25 pp",
  "categories": [
    "math.AG",
    "math.GR"
  ],
  "abstract": "Let $X$ be the surface $\\T\\times\\T$ where $\\T$ is the complex torus. This paper is the third in a series, studying the fundamental group of the Galois cover of $X$ \\wrt a generic projection onto $\\C\\P^2$. Van Kampen Theorem gives a presentation of the fundamental group of the complement of the branch curve, with 54 generators and more than 2000 relations. Here we introduce a certain natural quotient (obtained by identifying pairs of generators), prove it is a quotient of a Coxeter group related to the degeneration of $X$, and show that this quotient is virtually nilpotent.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-03-23T11:12:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J29"
    ],
    "keywords": [
      "fundamental group",
      "galois cover",
      "coxeter quotient",
      "van kampen theorem",
      "natural quotient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......4459M"
    }
  }
}