Universal orderability of Legendrian isotopy classes

TL;DR

This paper proves that non-negative Legendrian isotopy induces a partial order on the universal cover of Legendrian isotopy classes, with applications to Lorentz geometry and the Legendrian Low conjecture.

Contribution

It establishes a universal orderability result for Legendrian isotopy classes and applies it to problems in Lorentz geometry.

Findings

Non-negative Legendrian isotopy defines a partial order.

Application to Lorentz geometry and the Legendrian Low conjecture.

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.