Existence h-principle for Engel structures

• 成果类型: Article
• 署名作者: Casals, Roger; Luis Perez, Jose; del Pino, Alvaro; Presas, Francisco
• 署名单位: Massachusetts Institute of Technology (MIT); Autonomous University of Madrid; Universidad Carlos III de Madrid; Complutense University of Madrid; Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Ciencias Matematicas (ICMAT); CSIC - Instituto de Ciencia de Materiales de Madrid (ICMM)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-017-0732-6
• 发表日期: 2017
• 页码: 417-451
• 关键词: overtwisted contact structures; CLASSIFICATION; foliations

摘要

In this article we prove that the inclusion of the space of Engel structures of a smooth 4-manifold into the space of full flags of its tangent bundle induces surjections in all homotopy groups. In particular, we construct Engel structures representing any given full flag.