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The Engel–Lutz twist and overtwisted Engel structures

Álvaro del Pino and Thomas Vogel

Geometry & Topology 24 (2020) 2471–2546
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.

Keywords
Engel structures, overtwisted, h-principle
Mathematical Subject Classification
Primary: 58A30
References
Publication
Received: 4 February 2019
Revised: 16 September 2019
Accepted: 31 December 2019
Published: 29 December 2020
Proposed: Yasha Eliashberg
Seconded: Paul Seidel, András I Stipsicz
Authors
Álvaro del Pino
Department of Mathematics
Utrecht University
Utrecht
Netherlands
Thomas Vogel
Mathematisches Institut der LMU
Universität München
München
Germany