Causality and Legendrian linking in higher dimensional and causally simple spacetimes

Recently Nemirovski and myself showed that causal relation of two events in a globally hyperbolic spacetime is equivalent to the non triviality of the Legendrian link of the spheres in the space of all light rays formed by the lights rays through the two event points.
The result was obtained under the condition that the universal cover of a Cauchy surface of the spacetime is not compact.
In this talk we review these results and discuss the generalization of them to the case of Cauchy surfaces with compact universal coverings. The last results are based on the contact Bott–Samelson Theorem of Fraunfelder, Labrousse and Schlenk.
If time permits we will discuss possible relations between causality and linking in causally simple spacetimes which are more general than globally hyperbolic ones.