3-dimensional Seiberg--Witten theory and mirror symmetry

3维Seiberg--Witten理论和镜像对称

• 批准号: 2620080
• 金额: --
• 依托单位: University of Edinburgh
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2620080
• 关键词: dimensional; Seiberg; Witten; theory; mirror

The 4-dimensional Seiberg--Witten invariants provide interesting numbers allowing one to study smooth structures on 4-manifolds. They possess the structure resembling that of a topological quantum field theory where to a 3-manifold one associates the monopole Floer homology and to a 4-manifold the Seiberg--Witten invariants. The goal of this project is todefine a fully extended 3-dimensional TQFT underlying simplified, 3-dimensional, Seiberg--Witten invariants. A guiding tool will be provided by the theory of 3-dimensional mirror symmetry relating them to the Rozansky--Witten invariants.

四维Seiberg-维滕不变量提供了有趣的数字，使人们能够研究光滑结构的4流形。他们拥有的结构类似的拓扑量子场论的3歧管的一个协会的ZeroFloer同源性和4歧管的Seiberg-维滕不变量。这个项目的目标是定义一个完全扩展的三维TQFT基础简化，三维，Seiberg-维滕不变量。一个指导工具将提供的理论，3维镜像对称有关他们的Rozansky-维滕不变量。