Existence of Engel structures

• 成果类型: Article
• 署名作者: Vogel, Thomas
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2009.169.79
• 发表日期: 2009
• 页码: 79-137
• 关键词: contact structures; CLASSIFICATION

摘要

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 M-1, M-2 satisfying a certain condition on the characteristic foliations, there is an Engel structure on M-1#M-2#(S-2 x S-2) which is closely related to the original Engel structures.