On the strong orderability of overtwisted 3-folds

TL;DR

This paper investigates the existence of positive loops of contactomorphisms in overtwisted contact 3-manifolds, providing a construction method for such loops in specific overtwisted structures.

Contribution

It introduces a new construction of positive loops of contactomorphisms in overtwisted contact 3-folds via contact fibered connected sums along transverse knots.

Findings

Positive loops exist in certain overtwisted contact structures.

Construction method for positive loops in overtwisted 3-folds.

Advances understanding of contactomorphism dynamics in overtwisted manifolds.

Abstract

In this article we address the existence of positive loops of contactomorphisms in overtwisted contact 3-folds. We present a construction of such positive loops in the contact fibered connected sum of certain contact 3-folds along transverse knots. In particular, we obtain positive loops of contactomorphisms in overtwisted contact structures.