Geometry & Topology 14 (2010) 611–626

DOI: 10.2140/gt.2010.14.611

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 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 Cont₀(ST^*M).

Keywords

Legendrian isotopy, causality

Mathematical Subject Classification

Primary: 53D35

Secondary: 53C50, 83C99

References

Publication

Received: 23 May 2009
Revised: 19 October 2009
Accepted: 16 November 2009
Published: 15 February 2010
Proposed: Leonid Polterovich
Seconded: Yasha Eliashberg, Danny Calegari

Authors