{
  "id": "math/0311040",
  "version": "v1",
  "published": "2003-11-04T18:11:49.000Z",
  "updated": "2003-11-04T18:11:49.000Z",
  "title": "Non-proper Actions of the Fundamental Group of a Punctured Torus",
  "authors": [
    "Virginie Charette"
  ],
  "comment": "14 pages, 4 figures",
  "categories": [
    "math.DG"
  ],
  "abstract": "Given an affine isometry of $\\R^3$ with hyperbolic linear part, its Margulis invariant measures signed Lorentzian displacement along an invariant spacelike line. In order for a group generated by hyperbolic isometries to act properly on $\\R^3$, the sign of the Margulis invariant must be constant over the group. We show that, in the case when the linear part is the fundamental group of a punctured torus, positivity of the Margulis invariant over any finite generating set does not imply that the group acts properly. This contrasts with the case of a pair of pants, where it suffices to check the sign of the Margulis invariant for a certain triple of generators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-11-04T18:11:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57S30",
      "57M60",
      "53C50"
    ],
    "keywords": [
      "fundamental group",
      "punctured torus",
      "non-proper actions",
      "linear part",
      "invariant measures signed lorentzian displacement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....11040C"
    }
  }
}