Volume 14, issue 1 (2010)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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 STM 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 Cont˜0(STM).

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