La courbe en huit sur les sph\`eres \`a pointes et le noeud de huit
Geometric Topology
2024-09-11 v1
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.
Keywords
Cite
@article{arxiv.2409.06532,
title = {La courbe en huit sur les sph\`eres \`a pointes et le noeud de huit},
author = {Pierre Dehornoy},
journal= {arXiv preprint arXiv:2409.06532},
year = {2024}
}
Comments
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