H 1 Which geodesic flows are left-handed?

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

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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 $S^3$

    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 28/04/14
    Date de captation : 27/11/13
    Collection : Research talks ; Dynamical Systems and Ordinary Differential Equations ; Topology
    Format : QuickTime (.mov) Durée : 01:05:24
    Domaine : Topology ; Dynamical Systems & ODE
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2013-11-27_Dehornoy.mp4

Informations sur la rencontre

Nom de la rencontre : Jean-Morlet Chair - Doctoral school : Young mathematicians in dynamical systems / Chaire Jean-Morlet - Ecole doctorale : Paroles aux jeunes chercheurs en systèmes dynamiques
Organisateurs de la rencontre : Dal'Bo, Françoise ; Funar, Louis ; Hasselblatt, Boris ; Schapira, Barbara
Dates : 25/11/13 - 29/11/13
Année de la rencontre : 2013
URL Congrès : https://hasselblatttroubetzkoy.weebly.co...

Citation Data

DOI : 10.24350/CIRM.V.18479303
Cite this video as: Dehornoy, Pierre (2013). Which geodesic flows are left-handed?. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18479303
URI : http://dx.doi.org/10.24350/CIRM.V.18479303


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