Non-negative Legendrian isotopy in ST∗M

Chernov, Vladimir¹ ; Nemirovski, Stefan²

¹ Department of Mathematics, Dartmouth College, 6188 Kemeny Hall, Hanover, NH 03755, USA
² Steklov Mathematical Institute, Gubkina 8, 119991 Moscow, Russia, Mathematisches Institut, Ruhr-Universität Bochum, Universitätsstraße 150, 44780 Bochum, Germany

Geometry & topology, Tome 14 (2010) no. 1, pp. 611-626.

Résumé

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 ${\widetilde{Cont}}_0\left(S{T}^{\ast }M\right)$.

Détail

DOI : 10.2140/gt.2010.14.611

Keywords: Legendrian isotopy, causality

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