Existence and classification of overtwisted contact structures in all dimensions

• 成果类型: Article
• 署名作者: Borman, Matthew Strom; Eliashberg, Yakov; Murphy, Emmy
• 署名单位: Stanford University; Massachusetts Institute of Technology (MIT)
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-016-0134-4
• 发表日期: 2015
• 页码: 281-361
• 关键词: Manifolds; TOPOLOGY; plastikstufe; 3-manifolds; 5-manifolds; geometry

摘要

We establish a parametric extension h-principle for overtwisted contact structures on manifolds of all dimensions, which is the direct generalization of the 3-dimensional result from [12]. It implies, in particular, that any closed manifold admits a contact structure in any given homotopy class of almost contact structures.