Geodesic flow, left-handedness, and templates

Abstract

We establish that, for every hyperbolic orbifold 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. 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.

Version accepted for publication (Algebraic & Geometric Topology), 60 pages

References in corpus (1)

• Templates for geodesic flows

Cited by in corpus (5)

• Templates for geodesic flows
• Minimum Quadratic Helicity States
• Coding of geodesics and Lorenz-like templates for some geodesic flows
• Modular knots, automorphic forms, and the Rademacher symbols for triangle groups
• First-return maps of Birkhoff sections of the geodesic flow