Geodesic flow, left-handedness, and templates

Abstract : We establish that, for every hyperbolic orbifold of type (2, q, ∞) 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.
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Preprints, Working Papers, ...
Version accepted for publication (Algebraic & Geometric Topology), 60 pages. 2011


https://hal.archives-ouvertes.fr/hal-00655422
Contributor : Pierre Dehornoy <>
Submitted on : Tuesday, November 25, 2014 - 5:13:45 PM
Last modification on : Thursday, April 23, 2015 - 1:41:43 PM

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  • HAL Id : hal-00655422, version 3
  • ARXIV : 1112.6296

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Pierre Dehornoy. Geodesic flow, left-handedness, and templates. Version accepted for publication (Algebraic & Geometric Topology), 60 pages. 2011. <hal-00655422v3>

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