Existence of Engel structures

• Autores: Thomas I. Vogel
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 169, Nº 1, 2009, págs. 79-137
• Idioma: inglés
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• Resumen

  • 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.