Groups, Geometry, and Dynamics

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Volume 11, Issue 4, 2017, pp. 1347–1376
DOI: 10.4171/GGD/431

Published online: 2017-12-07

Which geodesic flows are left-handed?

Pierre Dehornoy[1]

(1) Université Grenoble Alpes, France

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 cone points. As a consequence, on the unit tangent bundle to a 3-conic sphere, the lift of every finite collection of closed geodesics is a fibered link.

Keywords: Chirality, hyperbolic surface, knot, geodesic flow, Anosov flow, Markov partition, fibered knot, oben book decomposition

Dehornoy Pierre: Which geodesic flows are left-handed?. Groups Geom. Dyn. 11 (2017), 1347-1376. doi: 10.4171/GGD/431