Existence of Engel structures

Details Existence of Engel structures Existence of Engel structures

2004-11-10

arxiv.org/abs/math/0411217v1

Annals of Math. 169 (2009), 79--137

Mathematics

Geometric Topology

57 pages, 14 figures

Scientific paper

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 M_1,M_2 satisfying a certain condition on the characteristic foliation, there is an Engel structure on M_1#M_2#(S^2xS^2) which is closely related to the original Engel structures.

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