Existence of Engel structures

Original · EN

We develop a construction of Engel stuctures on 4-manifolds based on decompositions of manifolds into round handles. This allows us to show that all parallelizable 4-manifolds admit an Engel structure. We also show that, given two Engel manifolds M₁,M₂ satisfying a certain condition on the characteristic foliation, there is an Engel structure on M₁#M₂#(S²xS²) which is closely related to the original Engel structures.