Applications of holomorphic curves in symplectic topology

全纯曲线在辛拓扑中的应用

• 批准号: 2261120
• 金额: --
• 依托单位: University of Cambridge
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2261120
• 关键词: Applications; holomorphic; curves; symplectic; topology

This thesis will investigate applications of closed and open holomorphic curve invariants in symplectic topology. The key tools will be invariants related to quantum and symplectic cohomology and to Floer theory, and its algebraic structures. Basic questions to be addressed include properties of symplectomorphism groups, the action of symplectomorphisms on Lagrangian submanifolds, and connections to algebraic and tropical geometry and to mirror symmetry.

本文主要研究闭和开全纯曲线不变量在辛拓扑中的应用。关键的工具将是与量子和辛上同调和Floer理论及其代数结构相关的不变量。要解决的基本问题包括性质的symplectomorphism群体，行动symplectomorphisms拉格朗日子流形，并连接到代数和热带几何和镜像对称。

项目成果

Generalised cohomology and relatively exact Lagrangian submanifolds

广义上同调和相对精确的拉格朗日子流形

• DOI: 10.17863/cam.91722
• 发表时间: 2022
• 作者: Porcelli N

Families of relatively exact Lagrangians, free loop spaces and generalised homology

• DOI: 10.1007/s00029-023-00910-6
• 发表时间: 2024-04-01
• 期刊: SELECTA MATHEMATICA-NEW SERIES
• 影响因子: 1.4
• 作者: Porcelli，Noah W.