It is shown that if the universal cover of a manifold is an open manifold, then two different fibres of the spherical cotangent bundle cannot be connected by a non-negative Legendrian isotopy. This result is applied to the study of causality in globally hyperbolic spacetimes. It is also used to strengthen a result of Eliashberg, Kim and Polterovich on the existence of a partial order on .
"Non-negative Legendrian isotopy in $ST^*M$." Geom. Topol. 14 (1) 611 - 626, 2010. https://doi.org/10.2140/gt.2010.14.611