Contact orderability up to conjugation

TL;DR

This paper investigates the structure of the contact partial order on the orbits of contactomorphism groups' adjoint actions, focusing on non-compact convex at infinity contact manifolds.

Contribution

It explores the properties and remnants of the contact partial order in the context of non-compact convex at infinity contact manifolds.

Findings

Analysis of contact orderability in non-compact settings

Identification of conditions for orderability up to conjugation

Insights into the structure of contactomorphism group orbits

Abstract

We study in this paper the remnants of the contact partial order on the orbits of the adjoint action of contactomorphism groups on their Lie algebras. Our main interest is a class of non-compact contact manifolds, called convex at infinity.