Actions on trees, automorphism groups, free products and property FA

对树、自同构群、自由积和属性 FA 的操作

• 批准号: 1949273
• 金额: --
• 依托单位: University of Southampton
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2017
• 资助国家: 英国
• 起止时间: 2017 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-1949273
• 关键词: Actions; trees; automorphism; groups; free

This is a project in the area of geometric group theory, which studies the algebraic objects of groups via their actions on geometric objects. In particular, this project will be concerned with the algebraic information that can be gleaned from actions of discrete groups on trees. The aims are to combine the strongly geometric language of translation length functions, along with the more combinatorial descriptions of Bass to understand actions and their properties. The preliminary objectives will be to furnish a new proof that the LERF property passes to free products and to study the automorphism groups of free products and characterise when these groups have property FA. This is timely research as there has been a great deal of recent interest in the much stronger property T for automorphism groups of free groups.

这是几何群论领域的一个项目，它通过群对几何对象的作用来研究群的代数对象。特别是，这个项目将关注的代数信息，可以收集到的行动离散群体的树木。其目的是联合收割机的翻译长度函数的强几何语言，沿着随着更多的组合描述低音理解行动和他们的财产。初步的目标是提供一个新的证明，LERF性质传递到自由产品和研究的自同构群的自由产品和ERF时，这些群体有性质FA。这是及时的研究，因为最近对自由群的自同构群的强得多的性质T有很大的兴趣。

项目成果

Serre's Property (FA) for automorphism groups of free products

自由积自同构群的塞尔性质 (FA)

• DOI: 10.1515/jgth-2019-0140
• 发表时间: 2021
• 期刊: Journal of Group Theory
• 影响因子: 0.5
• 作者: Andrew N

Free-by-cyclic groups, automorphisms and actions on nearly canonical trees

自由循环群、自同构和近规范树上的作用

• DOI: 10.1016/j.jalgebra.2022.03.033
• 发表时间: 2022
• 期刊: Journal of Algebra
• 影响因子: 0.9
• 作者: Andrew N

A Bass-Serre theoretic proof of a theorem of Romanovskii and Burns

Romanovskii 和 Burns 定理的 Bass-Serre 理论证明

• DOI: 10.1080/00927872.2022.2149764
• 发表时间: 2022
• 期刊: Communications in Algebra
• 影响因子: 0.7
• 作者: Andrew N