Geodesic flow, left-handedness, and templates

Pierre Dehornoy (1)

1 IF - Institut Fourier

We establish that, for every hyperbolic orbifold of type (2, q, ∞) 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. 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.

Mots clés: linking number; template; geodesic; left-handed flow; knot

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

Pierre Dehornoy. Geodesic flow, left-handedness, and templates. Algebraic and Geometric Topology, 2015, 15, pp.1525-1597. ⟨10.2140/agt.2015.15.1525⟩. ⟨hal-00655422v3⟩