Abstract
We establish that for every hyperbolic orbifold of type and for every orbifold of type , the geodesic flow on the unit tangent bundle is left handed. This implies that the link formed by every collection of periodic orbits bounds a Birkhoff section for the geodesic flow, and is a fibered link. We also prove similar results for the torus with any flat metric. We also observe that the natural extension of the conjecture to arbitrary hyperbolic surfaces (with non-trivial homology) is false.
Citation
Pierre Dehornoy. "Geodesic flow, left-handedness and templates." Algebr. Geom. Topol. 15 (3) 1525 - 1597, 2015. https://doi.org/10.2140/agt.2015.15.1525
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