Existence of Engel structures
Abstract
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.
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