Algebraic Structures on Symplectic Homology and Their Applications

这个项目的主题是辛同调，一个不变量的辛流形与接触型边界。这项建议有两个目标。第一个是通过引入额外的代数结构来增强这个理论。第二个目标是将这些新结构应用于辛拓扑中的特定问题：拉格朗日嵌入和浸入，接触嵌入，辛填充拓扑以及与奇点理论的关系。

The subject of this project is symplectic homology, an invariant of symplectic manifolds with contact type boundary. This proposal has two goals. The first one is to enhance this theory by introducing additional algebraic structures. The second goal is to apply these new structures to specific problems in symplectic topology: Lagrangian embeddings and immersions, contact embeddings, topology of symplectic fillings, and relations to the theory of singularities.