A simple construction of positive loops of Legendrians

TL;DR

This paper presents a straightforward method to construct positive loops of Legendrian submanifolds, extending previous results and exploring conditions for their contractibility.

Contribution

It introduces a simple construction technique for positive Legendrian loops and partially generalizes Liu's result on loose Legendrians.

Findings

Positive loops of Legendrians can be constructed in multiple cases.

Loose Legendrians admit positive loops under mild conditions.

Constructed loops can be contractible with additional topological assumptions.

Abstract

We construct positive loops of Legendrian submanifolds in several instances. In particular, we partially recover G. Liu's result stating that any loose Legendrian admits a positive loop, under some mild topological assumptions on the Legendrian. Moreover, we show contractibility of the constructed loops under an extra topological assumption.