Non-negative Legendrian isotopy in $ST^*M$

Details Non-negative Legendrian isotopy in $ST^*M$ Non-negative Legendrian isotopy in $ST^*M$

2009-05-07

arxiv.org/abs/0905.0983v1

Geometry & Topology 14 (2010), 611-626

Mathematics

Symplectic Geometry

10 pages

Scientific paper

10.2140/gt.2010.14.611

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 $ST^*M$ 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 $\widetilde{\mathrm{Cont}}_0 (ST^*M)$.

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