Legendrian linking, Causality in classical and in Generalized spacetimes via Virtual Legendrian Linking.

par Vladimir Chernov

lundi 19 avr. 2027, 14:00 → 15:00 Europe/Paris

Salle de séminaires IRMA

Jointly with Stefan Nemrovski in our GAFA, GT and GP paper we showed Legendrian linking of the spheres of light rays through the two points does (nearly always) tell if the two event points in the universe are causally related, that is if they know of each other existence. We review these results and related Bott-Samelson type results of Nemirovski and myself and of Fraunenfelder-Labrousse-Shlenk. After that we introduce generalized spacetime that are singular Lorentz manifolds whose critical levels of a singular timelike Morse function cut them into globally hyperbolic pieces. Strong Cosmic censorship conjecture of Penrose suggests that if you delete black holes along horizons then what is left is globally hyperbolic. We introduce virtual Legendrian linking coming from the unit cotangent bundles of the spacetlike sections of such pieces and jointly with Sadykov we formulate the conjectures relating causality in generalized spacetimes to virtual Legendrian linking. In the remaining time we explore the theory results on virtual Legendrian links of Sadykov and myself.