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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Journal articles
Algebraic and Geometric Topology, Mathematical Sciences Publishers, 2015, 15, pp.1525-1597. <10.2140/agt.2015.15.1525>


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 21, 2016 - 3:40:48 PM

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Pierre Dehornoy. Geodesic flow, left-handedness, and templates. Algebraic and Geometric Topology, Mathematical Sciences Publishers, 2015, 15, pp.1525-1597. <10.2140/agt.2015.15.1525>. <hal-00655422v3>

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