Engel structures

April 17 to April 21, 2017

at the

American Institute of Mathematics, San Jose, California

organized by

Yakov Eliashberg, Dieter Kotschick, Emmy Murphy, and Thomas Vogel

Original Announcement

This workshop will be devoted to the emerging theory of Engel structures on four-manifolds, especially questions of rigidity versus flexibility, and its (potential) connections with contact topology, dynamics, and four-dimensional differential topology and gauge theory.

The main purpose of the workshop is to review some recent progress on the existence of Engel structures and to stimulate further research by bringing into focus geometrically interesting questions and by making connections to the modern theory of four-manifolds. With this goal in mind, the workshop will bring together people with different areas of expertise: those responsible for previous work on Engel structures, experts in contact topology and related topics, and experts on four-manifolds. Questions of a more dynamical flavor as well as questions pertaining to subriemannian geometry may also be discussed.

The main topics for the workshop are:

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Papers arising from the workshop:

Complex Engel Structures
by  Zhiyong Zhao
Lagrangian Engel Structures
by  Zhiyong Zhao
Geometry and dynamics of Engel structures
by  Yoshihiko Mitsumatsu
Notes on open book decompositions for Engel structures
by  Vincent Colin, Francisco Presas, and Thomas Vogel
Classification of Engel knots
by  Roger Casals, and Alvaro del Pino,  Math. Ann. 371 (2018), no. 1-2, 391–404  MR3788852
The Engel-Lutz twist and overtwisted Engel structures
by  Alvaro del Pino, and Thomas Vogel