Existence of Engel structures

By T. Vogel. 2004

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We develop a construction of Engel structures 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 foliations, there is an Engel structure on M1#M2#(S2 ×S2) which is closely related to the original Engel structures.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/68344d3ba90b07082e8e75adc06c0c9ec2956c41