Geodesic flow, left-handedness and templates

Dehornoy, Pierre

doi:10.2140/agt.2015.15.1525

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Geodesic flow, left-handedness and templates

Pierre Dehornoy

Algebraic & Geometric Topology 15 (2015) 1525–1597

DOI: 10.2140/agt.2015.15.1525

Abstract

We establish that for every hyperbolic orbifold of type $(2, q, \infty)$ and for every orbifold of type $(2, 3, 4 g + 2)$ , 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 $(i i)$ 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/

Volume 15, issue 3 (2015)