Topology of moduli spaces

模空间的拓扑

• 批准号: 2597647
• 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: 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-2597647
• 关键词: Topology; moduli; spaces

There are many ways of forming spaces of mathematical objects, or of subobjects of some fixed one, and it is usually of considerable interest to examine the topology of such spaces. Examples are moduli spaces of smooth manifolds, giving a new perspective on the study of diffeomorphism groups, classical examples such as configuration spaces and their variants, or spaces of Riemannian metrics subject to curvature conditions. Increasingly sophisticated techniques from homotopy theory are being used to examine such spaces. This project will deploy such methods to investigate questions such as: can distinct mathematical objects have equivalent moduli spaces?

形成数学对象的空间或某些固定对象的子对象的空间的方法有很多种，并且通常对检查此类空间的拓扑结构非常感兴趣。例子有光滑流形的模空间，为微分同胚群的研究提供了新的视角，经典的例子如配置空间及其变体，或受曲率条件影响的黎曼度量空间。来自同伦理论的日益复杂的技术被用来检查这些空间。该项目将部署此类方法来研究诸如以下问题：不同的数学对象是否可以具有等效的模空间？