#### Volume 14, issue 1 (2010)

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

### Vladimir Chernov and Stefan Nemirovski

Geometry & Topology 14 (2010) 611–626
##### 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 ${\stackrel{˜}{Cont}}_{0}\left(S{T}^{\ast }M\right)$.

##### Keywords
Legendrian isotopy, causality
##### Mathematical Subject Classification 2000
Primary: 53D35
Secondary: 53C50, 83C99