Exact Lagrangian submanifolds in simply-connected cotangent bundles

• 成果类型: Article
• 署名作者: Fukaya, Kenji; Seidel, Paul; Smith, Ivan
• 署名单位: Kyoto University; Massachusetts Institute of Technology (MIT); University of Cambridge
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-007-0092-8
• 发表日期: 2008
• 页码: 1-27
• 关键词: homology

摘要

We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second Stiefel-Whitney class of the Lagrangian submanifold) we prove such submanifolds are Floer-cohomologically indistinguishable from the zero-section. This implies strong restrictions on their topology. An essentially equivalent result was recently proved independently by Nadler [16], using a different approach.