Which geodesic flows are left-handed ?

Pierre Dehornoy (1)

1 IF - Institut Fourier

We prove that the geodesic flow on the unit tangent bundle to a hyperbolic 2-orbifold is left-handed if and only if the orbifold is a sphere with three conic points. As a consequence, on the unit tangent bundle to a 3-conic sphere, the lift of every finite collection of closed geodesics that is zero in integral homology is the binding of an open book decomposition.

Mots clés: open book; fibered knot; geodesic; flow; surface; knot

Domaines: Topologie géométrique [math.GT]; Systèmes dynamiques [math.DS]

Pierre Dehornoy. Which geodesic flows are left-handed ?. 2015. ⟨hal-01102467v1⟩