The Engel-Lutz twist and overtwisted Engel structures

TL;DR

This paper introduces a modification procedure for Engel structures inspired by the Lutz twist, enabling the definition of overtwisted discs and establishing a complete h-principle for overtwisted Engel structures.

Contribution

It presents a new modification technique for Engel structures and proves an h-principle for overtwisted Engel structures with fixed overtwisted discs.

Findings

Defined Engel overtwisted discs

Proved a complete h-principle for overtwisted Engel structures

Established a modification procedure analogous to the Lutz twist

Abstract

We introduce a modification procedure for Engel structures that is reminiscent of the Lutz twist in 3-dimensional Contact Topology. This notion allows us to define what an Engel overtwisted disc is, and to prove a complete h-principle for overtwisted Engel structures with fixed overtwisted disc.