Algebraic structure of Tate cohomology

Tate 上同调的代数结构

• 批准号: 2610220
• 金额: --
• 依托单位: University of Sheffield
• 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-2610220
• 关键词: Algebraic; structure; Tate; cohomology

An important invariant in homotopical algebra and equivariant algebraic topology will be explored to understand the algebraic structure present and how this structure can be used in applications. The Tate cohomology of a group combines the standard homology and cohomology groups into a single invariant. It can be viewed as a completed version of the Ext functor in a suitable setting. The usual Ext has a product structure and this is known to be part of a much more intricate structure called an A-infinity algebra. The project will investigate the corresponding structure, and other related algebraic structure, for complete Ext.

我们将探索同伦代数和等变代数拓扑中的一个重要不变量，以了解目前存在的代数结构以及这种结构如何在应用中使用。群的Tate上同调将标准同调群和上同调群合并为一个不变量。在适当的设置下，它可以被视为Ext函数器的完整版本。通常的Ext有一个乘积结构，而这是一个更复杂的结构的一部分，称为A-无穷大代数。该项目将调查相应的结构，以及其他相关的代数结构，以完成Ext。