Geodesic flow, left-handedness, and templates

Details Geodesic flow, left-handedness, and templates Geodesic flow, left-handedness, and templates

2011-12-29

arxiv.org/abs/1112.6296v2

Mathematics

Geometric Topology

Second version with 58 pages and 31 figures. The main theorem now applies to an infinite family of compact orbifolds. Also the

Scientific paper

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.

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