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Post-edited Which geodesic flows are left-handed?

Auteurs : Dehornoy, Pierre (Auteur de la Conférence)
CIRM (Editeur )

 Loading the player... Lorenz vector field surface of section first-return map intersection pairing Schwartzmann asymptotic cycle Fuller-Fried theorem Birkhoff section Hopf flow geodesic flow left-handed flows Ghys definition SO(3) negatively curved orbifold geodesic flow homology sphere unit tangent bundle surgery presentation template

Résumé : Left-handed flows are 3-dimensional flows which have a particular topological property, namely that every pair of periodic orbits is negatively linked. This property (introduced by Ghys in 2007) implies the existence of as many Bikrhoff sections as possible, and therefore allows to reduce the flow to a suspension in many different ways. It then becomes natural to look for examples. A construction of Birkhoff (1917) suggests that geodesic flows are good candidates. In this conference we determine on which hyperbolic orbifolds is the geodesic flow left-handed: the answer is that yes if the surface is a sphere with three cone points, and no otherwise.
dynamical system - geodesic flow - knot - periodic orbit - global section - linking number - fibered knot

Codes MSC :
37C10 - Vector fields, flows, ordinary differential equations
37C15 - Topological and differentiable equivalence, conjugacy, invariants, moduli, classification
37C27 - periodic orbits of vector fields and flows
57M25 - Knots and links in $S^3$, {For higher dimensions, See 57Q45}

 Informations sur la Vidéo Réalisateur : Hennenfent, Guillaume Langue : Anglais Date de publication : 28/04/14 Date de captation : 27/11/13 Collection : Research talks Format : QuickTime (.mov) Durée : 01:05:24 Domaine : Topology ; Dynamical Systems & ODE Audience : Chercheurs ; Doctorants , Post - Doctorants Download : http://videos.cirm-math.fr/2013-11-27_Dehornoy.mp4 Informations sur la rencontre Nom du congrès : Jean-Morlet Chair - Doctoral school : Young mathematicians in dynamical systems / Chaire Jean-Morlet - Ecole doctorale : Paroles aux jeunes chercheurs en systèmes dynamiquesOrganisteurs Congrès : Dal'Bo, Françoise ; Funar, Louis ; Hasselblatt, Boris ; Schapira, BarbaraDates : 25/11/13 - 29/11/13 Année de la rencontre : 2013 URL Congrès : http://hasselblatttroubetzkoy.weebly.com... Citation DataDOI : 10.24350/CIRM.V.18479303Cite this video as: Dehornoy, Pierre (2013).Which geodesic flows are left-handed?. CIRM . Audiovisual resource .doi:10.24350/CIRM.V.18479303URI : http://dx.doi.org/10.24350/CIRM.V.18479303

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