Classifying spaces, proper actions and stable homotopy theory

空间分类、适当作用和稳定同伦理论

• 批准号: EP/X038424/1
• 负责人: Irakli Patchkoria
• 金额: $ 38.01万
• 依托单位: University of Aberdeen
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FX038424%2F1
• 关键词: Classifying; spaces; proper; actions; stable

Primary goal of this project is to compute invariants of discrete groups coming from stable homotopy theory. Secondary goal is to explore connections of these computations with number theory. The project deals with invariants of infinite discrete groups coming from stable homotopy theory, such as Morava K-theories and Morava E-theories. These invariants generalise the classical Euler characteristic and topological K-theory. For finite groups they are well-known and studied by Hopkins-Kuhn-Ravenel. For K-theory these invariants for infinite groups were computed by Lück and coathors. We plan to generalise both these computations.For Morava K-theories of infinite groups we expect to obtain a formula for the Morava K-theoretic Euler characteristic using centralisers. For Morava E-theory we plan to generalise the Hopkins-Kuhn-Ravenel character theory from finite to infinite groups. Finally, we will apply these results to concrete groups. Concrete formulas coming out of these should be of number theoretic nature. Some of them will contain values of Dedekind and Riemann zeta functions.

该项目的主要目标是计算来自稳定同伦理论的离散群的不变量，次要目标是探索这些计算与数论的联系该项目处理来自稳定同伦理论的无限离散群的不变量，例如 Morava K。 -理论和 Morava E 理论。这些不变量概括了经典的欧拉特性和拓扑 K 理论，它们是众所周知的，并由 Hopkins-Kuhn-Ravenel 进行了研究。 K 理论无限群的这些不变量是由 Lück 和 Coathors 计算的。我们计划推广这两种计算。对于无限群的 Morava K 理论，我们期望使用 Morava 中心化器获得 Morava K 理论欧拉特征的公式。 E 理论我们计划将 Hopkins-Kuhn-Ravenel 特征理论从有限群推广到无限群，最后，我们将把这些结果应用到具体的群中。应该具有数论性质。其中一些将包含戴德金和黎曼 zeta 函数的值。