La courbe en huit sur les sphères à pointes et le noeud de huit

Abstract

We show that, in the unit tangent bundle of a hyperbolic orbisphere with cone points of order 3, 3, 4, the lift of the shortest periodic geodesic is homeomorphic to the complement of the figure-eight knot in the 3-sphere. The proof eventually relies on the computation of some linking numbers.

These expository notes present a picturial and dynamical proof of a theorem for which we claim no novelty. 14 pages, in French language, 10 figures

References in corpus (3)

• Lectures on open book decompositions and contact structures
• Hyperbolic models of transitive topologically Anosov flows in dimension three
• Complex vs convex Morse functions and geodesic open books