{
  "id": "0904.1194",
  "version": "v1",
  "published": "2009-04-07T19:02:51.000Z",
  "updated": "2009-04-07T19:02:51.000Z",
  "title": "A classification of special 2-fold coverings",
  "authors": [
    "Anne Bauval",
    "Daciberg L Goncalves",
    "Claude Hayat",
    "Maria Herminia de Paula Leite Mello"
  ],
  "comment": "This is the version published by Geometry & Topology Monographs on 29 April 2008",
  "journal": "Geom. Topol. Monogr. 14 (2008) 27-47",
  "doi": "10.2140/gtm.2008.14.27",
  "categories": [
    "math.AT",
    "math.GT"
  ],
  "abstract": "Starting with an O(2)-principal fibration over a closed oriented surface F_g, g>=1, a 2-fold covering of the total space is said to be special when the monodromy sends the fiber SO(2) = S^1 to the nontrivial element of Z_2. Adapting D Jonhson's method [Spin structures and quadratic forms on surfaces, J London Math Soc, 22 (1980) 365-373] we define an action of Sp(Z_2,2g), the group of symplectic isomorphisms of (H_1(F_g;Z_2),.), on the set of special 2-fold coverings which has two orbits, one with 2^{g-1}(2^g+1) elements and one with 2^{g-1}(2^g-1) elements. These two orbits are obtained by considering Arf-invariants and some congruence of the derived matrices coming from Fox Calculus. Sp(Z_2,2g) is described as the union of conjugacy classes of two subgroups, each of them fixing a special 2-fold covering. Generators of these two subgroups are made explicit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-07T19:02:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R15",
      "53C27"
    ],
    "keywords": [
      "classification",
      "london math soc",
      "total space",
      "symplectic isomorphisms",
      "monodromy sends"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}