Punctured holomorphic curves and Lagrangian embeddings

• 成果类型: Article
• 署名作者: Cieliebak, K.; Mohnke, K.
• 署名单位: University of Augsburg; Humboldt University of Berlin
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-017-0767-8
• 发表日期: 2018
• 页码: 213-295
• 关键词: symplectic hypersurfaces; maslov class; Transversality; submanifolds; dimension; RIGIDITY; index; tori

摘要

We use a neck stretching argument for holomorphic curves to produce symplectic disks of small area and Maslov class with boundary on Lagrangian submanifolds of nonpositive curvature. Applications include the proof of Audin's conjecture on the Maslov class of Lagrangian tori in linear symplectic space, the construction of a new symplectic capacity, obstructions to Lagrangian embeddings into uniruled symplectic manifolds, a quantitative version of Arnold's chord conjecture, and estimates on the size of Weinstein neighbourhoods. The main technical ingredient is transversality for the relevant moduli spaces of punctured holomorphic curves with tangency conditions.