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

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。

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.