Algebraic invariants of spaces with group action

群作用空间的代数不变量

• 批准号: 2274577
• 金额: --
• 依托单位: University of Warwick
• 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-2274577
• 关键词: Algebraic; invariants; spaces; group; action

The project lies in the area of geometry and topology. A range of geometricobjects are relevant arising from homotopy theory, representation theory andalgebra more broadly.To start with one may consider invariants that are invariant under feformations,but one may go on to build the algebraic invariants using more geometricmethods. In certain circumstances these two approaches converge and acomplete model can be built in an algebraic setting. This is in the context of thefact that equivariant homotopy theory is now quite well understood and readyfor this treatment. The aim is to give accessible means of calculation and accessto broad structural features. The test in this particular case is whethercalculations can be completed. For example one may seek a form of higher Smiththeory along the lines of Dwyer and Wilkerson.

该项目属于几何和拓扑学领域。从同伦理论、表示理论和更广泛的代数中产生的一系列几何对象是相关的。首先，人们可以考虑在变形下不变的不变量，但人们可以继续使用更多的几何方法来构建代数不变量。在某些情况下，这两种方法收敛，在代数环境下可以建立一个完整的模型。这是在这样一个事实的背景下，即等变同伦理论现在已经被很好地理解并准备好进行这种处理。其目的是提供可访问的计算方法和获取广泛的结构特征。在这种特殊情况下的测试是是否可以完成计算。例如，人们可以沿着德怀尔和威尔克森的路线寻求一种更高形式的史密斯理论。