Universal orderability of Legendrian isotopy classes

Abstract

It is shown that non-negative Legendrian isotopy defines a partial order on the universal cover of the Legendrian isotopy class of the fibre of the spherical cotangent bundle of any manifold. This result is applied to Lorentz geometry in the spirit of the authors' earlier work on the Legendrian Low conjecture.

13 pages; V.2 - minor edits, reference added; V.3 - editorial changes, references added

References in corpus (3)

• Linking and causality in globally hyperbolic spacetimes
• Quasi-morphisms on contactomorphism groups and contact rigidity
• Geometric structures on contactomorphism groups and contact rigidity in jet spaces

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• The space of light rays: Causality and $L$-boundary
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• Legendrian links and déjà vu moments
• Topological consequences of null-geodesic refocusing and applications to $Z^x$ manifolds