Non-negative Legendrian isotopy in ST∗M

Chernov, Vladimir; Nemirovski, Stefan

doi:10.2140/gt.2010.14.611

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

Vladimir Chernov and Stefan Nemirovski

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 $S T^{*} M$ 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 ${\tilde{Cont}}_{0} (S T^{*} M)$ .

Keywords

Legendrian isotopy, causality

Mathematical Subject Classification 2000

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 and Danny Calegari

Authors

Vladimir Chernov
Department of Mathematics Dartmouth College 6188 Kemeny Hall, Hanover, NH 03755 USA

Stefan Nemirovski
Steklov Mathematical Institute Gubkina 8 119991 Moscow Russia	Mathematisches Institut Ruhr-Universität Bochum Universitätsstraße 150 44780 Bochum Germany

Volume 14, issue 1 (2010)