Punctured Holomorphic Curves in Symplectic Geometry

辛几何中的穿孔全纯曲线

• 批准号: 5407273
• 负责人: Professor Dr. Kai Cieliebak
• 金额: --
• 依托单位: Institut für Mathematik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2003
• 资助国家: 德国
• 起止时间: 2002-12-31 至 2009-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5407273?language=en
• 关键词: Punctured; Holomorphic; Curves; Symplectic; Geometry

The aim of this project is to systematically apply punctured holomorphic curves to questions in symplectic geometry. This is particularly promising for Lagrangian embeddings, where we expect new results on Lagrangian intersections, intersections of Lagrangian submanifolds with balls, Maslov class and symplectic area class rigidity, and unknottedness in dimension four. Moreover, we will lay the foundations for further applications by studying punctured holomorphic curves in cotangent bundles and their relations to closed geodesics and harmonic maps.

这个项目的目的是系统地应用穿孔全纯曲线在辛几何中的问题。这对于拉格朗日嵌入尤其有希望，我们期待在拉格朗日交集，拉格朗日子流形与球的交集，马斯洛夫类和辛面积类刚性，以及四维的不结性方面的新结果。此外，我们将通过研究共切束中的穿孔全纯曲线及其与封闭测地线和调和映射的关系，为进一步的应用奠定基础。