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.

Higgs丛的模空间具有许多当前非常感兴趣的几何和拓扑性质。在保证空间光滑的某些条件下，关于这个空间的拓扑已经知道了很多，然而当这些条件被去掉时，知道的还不是很多。这个项目的目的是利用最近发展的奇异空间上的Morse理论框架来研究这个问题，并在以前未知的出现奇点的情况下发展关于这个模空间的拓扑不变量的新结果。