Punctured Holomorphic Curves in Symplectic Geometry

这个项目的目的是系统地应用穿孔全纯曲线的问题辛几何。这是特别有前途的拉格朗日嵌入，我们期待新的结果，拉格朗日相交，拉格朗日子流形与球，马斯洛夫类和辛面积类刚性，和unknottedness在第四个维度的交叉。此外，通过研究余切丛中的穿孔全纯曲线及其与闭测地线和调和映射的关系，为进一步的应用奠定了基础。

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.