Bordifying outer spaces for right-angled Artin groups

为直角 Artin 群界定外部空间

• 批准号: 2105827
• 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: 2018
• 资助国家: 英国
• 起止时间: 2018 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2105827
• 关键词: Bordifying; outer; spaces; right; angled

For any arithmetic group, including SL(n,Z), Borel and Serre defined a bordification of the associated symmetric space; this is an extension of the symmetric space with a proper cocompact action of the arithmetic group, so can be used to study the cohomology and coarse geometry of the group. For the group of outer automorphisms of a free group, an analogous bordification of Outer space was constructed by Bestvina and Feighn. Right-angled Artin groups generalize both free and free abelian groups. Charney and Vogtmann have defined an outer space on which the outer automorphism group of any right-angled Artin group acts, generalizing both the symmetric space for SL(n,Z) and Outer space for Out(F_n), and the goal of this project is to construct an analogous bordification of this general outer space.

对于任何算术群，包括SL（n，Z），Borel和Serre定义了相关对称空间的边化;这是对称空间的扩张，具有算术群的适当上紧作用，因此可以用来研究群的上同调和粗糙几何。对于自由群的外自同构群，Bestern和Feigh构造了类似的外空间边界化。直角阿廷群推广了自由和自由阿贝尔群。Charney和Vogtmann定义了任何直角Artin群的外自同构群作用于其上的外空间，推广了SL（n，Z）的对称空间和Out（F_n）的外空间，该项目的目标是构建一个类似的边界化这个一般的外空间。