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arXiv · 1112.6296

Geodesic flow, left-handedness, and templates

Pierre Dehornoy
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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.

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Pierre Dehornoy. 2014-12-05. Geodesic flow, left-handedness, and templates. https://doi.org/10.2140/agt.2015.15.1525

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