Handlebody construction of Stein surfaces

• 成果类型: Article
• 署名作者: Gompf, RE
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/121005
• 发表日期: 1998
• 页码: 619-693
• 关键词: contact structures; exotic r4s; INVARIANTS; 3-manifolds; MANIFOLDS; geometry; TOPOLOGY

摘要

The topology of Stein surfaces and contact 3-manifolds is studied by means of handle decompositions. A simple characterization of homeomorphism types of Stein surfaces is obtained-they correspond to open handlebodies with all handles of index less than or equal to 2. An uncountable collection of exotic R-4's is shown to admit Stein structures. New invariants of contact S-manifolds are produced, including a complete (and computable) set of invariants for determining the homotopy class of a 2-plane field on a 3-manifold. These invariants are applicable to Seiberg-Witten theory. Several families of oriented 3-manifolds are examined, namely the Seifert fibered spaces and all surgeries on various links in S-3, and in each case it is seen that most members of the family are the oriented boundaries of Stein surfaces.