{
  "id": "1112.6296",
  "version": "v3",
  "published": "2011-12-29T12:54:30.000Z",
  "updated": "2014-12-05T08:13:20.000Z",
  "title": "Geodesic flow, left-handedness, and templates",
  "authors": [
    "Pierre Dehornoy"
  ],
  "comment": "Version accepted for publication (Algebraic & Geometric Topology), 60 pages",
  "categories": [
    "math.GT",
    "math.DS"
  ],
  "abstract": "We establish that, for every hyperbolic orbifold of type (2, q, $\\infty$) and for every orbifold of type (2, 3, 4g+2), the geodesic flow on the unit tangent bundle is left-handed. This implies that the link formed by every collection of periodic orbits (i) bounds a Birkhoff section for the geodesic flow, and (ii) is a fibered link. We also prove similar results for the torus with any flat metric. Besides, we observe that the natural extension of the conjecture to arbitrary hyperbolic surfaces (with non-trivial homology) is false.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-11T18:32:46.000Z",
      "abstract": "We establish that, for every hyperbolic orbifolds of type $(2,q,\\infty)$ and for every orbifold of type $(2,3,4g+2)$, the geodesic flow on the unit tangent bundle is left-handed. This implies that the link formed by every collection of periodic orbits $(i)$ bounds a Birkhoff section for the geodesic flow, and $(ii)$ is a fibered link. These results support a conjecture of Ghys that these properties hold for every 2-dimensional hyperbolic orbifold that is a homology sphere. We also prove similar results for the torus with any flat metric. Besides, we observe that the natural extension of the conjecture to arbitrary hyperbolic surfaces (with non-trivial homology) is false.",
      "comment": "Second version with 58 pages and 31 figures. The main theorem now applies to an infinite family of compact orbifolds. Also the use of a computer in the main proof has been cancelled",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-12-05T08:13:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geodesic flow",
      "left-handedness",
      "unit tangent bundle",
      "arbitrary hyperbolic surfaces",
      "non-trivial homology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 60,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.6296D"
    }
  }
}