Moduli space of Higgs Bundles

希格斯丛集的模空间

• 批准号: 2742617
• 金额: --
• 依托单位: University of York
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2742617
• 关键词: Moduli; space; Higgs; Bundles

The moduli space of Higgs bundles has a number of geometric and topological properties that are of great current interest. Quite a lot is known about the topology of this space under certain conditions that guarantee that it is smooth, however not much is known when these conditions are removed. The aim of this project is to use a recently developed framework for Morse theory on singular spaces to investigate this problem and to develop new results about topological invariants of this moduli space in previously unknown cases where singularities appear.

希格斯捆绑包的模量空间具有许多当前感兴趣的几何和拓扑特性。在某些条件下，该空间的拓扑已知很多，这些条件可以保证它是光滑的，但是当去除这些条件时，尚不清楚。该项目的目的是在奇异空间上使用最近开发的莫尔斯理论框架来研究这个问题，并在以前未知的奇异案例中，开发有关该模量空间拓扑不变的新结果。