Geodesic
Geodesic flow, left-handedness and templates
Dehornoy, Pierre1
1Institut Fourier, 100 rue des maths, BP74, 38402 St. Martin-d’Hères, France
Algebraic and Geometric Topology, Tome 15 (2015) no. 3, pp. 1525-1597
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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.

DOI : 10.2140/agt.2015.15.1525
Classification : 37D40, 57M20, 37D45, 37B50
Keywords: geodesic, knot, template, linking number, left handed flow

Dehornoy, Pierre  1

1 Institut Fourier, 100 rue des maths, BP74, 38402 St. Martin-d’Hères, France 
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Dehornoy, Pierre. Geodesic flow, left-handedness and templates. Algebraic and Geometric Topology, Tome 15 (2015) no. 3, pp. 1525-1597. doi: 10.2140/agt.2015.15.1525

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