Non-negative Legendrian isotopy in $S{T}^{\ast }M$

Abstract

It is shown that if the universal cover of a manifold $M$ is an open manifold, then two different fibres of the spherical cotangent bundle $S{T}^{\ast }M$ 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 ${\widetilde{\mathrm{Cont}}}_0(S{T}^{\ast }M)$.

10 pages

References in corpus (3)

• Geometry of contact transformations and domains: orderability versus squeezing
• Legendrian links, causality, and the Low conjecture
• Linking and causality in globally hyperbolic spacetimes

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