Abstract - Vogel - Existence of Engel structures

Thomas Vogel (IAS/UPenn): Existence of Engel stucturess

Abstract:

Engel structures are non-integrable plane fields on 4-manifolds who share many properties with contact structures. The existence of an Engel structure on a manifolds leads to strong restrictions on the topology of the manifold: Under certain orientation assumptions the tangent bundle of the manifold is trivial.

In this talk we develop a construction which shows that the converse is also true: Every 4-manifold with trivial tangent bundle admits an Engel structure.