#### Volume 15, issue 3 (2015)

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Geodesic flow, left-handedness and templates

### Pierre Dehornoy

Algebraic & Geometric Topology 15 (2015) 1525–1597
##### Abstract

We establish that for every hyperbolic orbifold of type $\left(2,q,\infty \right)$ and for every orbifold of type $\left(2,3,4g+2\right)$, the geodesic flow on the unit tangent bundle is left handed. This implies that the link formed by every collection of periodic orbits $\left(i\right)$ bounds a Birkhoff section for the geodesic flow, and $\left(ii\right)$ 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.

##### Keywords
geodesic, knot, template, linking number, left handed flow
##### Mathematical Subject Classification 2010
Primary: 37D40, 57M20
Secondary: 37D45, 37B50