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 (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. 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
References
Publication
Received: 18 February 2014
Revised: 4 August 2014
Accepted: 18 October 2014
Published: 19 June 2015
Authors
Pierre Dehornoy
Institut Fourier
100 rue des maths
BP74
38402 St. Martin-d’Hères
France
http://www-fourier.ujf-grenoble.fr/~dehornop/