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

这是几何群论领域的一个项目，它通过群在几何对象上的作用来研究群的代数对象。特别是，这个项目将关注可以从树上离散群的作用中收集到的代数信息。其目的是将平移长度函数的强几何语言与Bass的更多组合描述结合起来，以理解动作及其性质。初步的目的将是提供一个新的证明，即LERF性质传递到自由积，并研究自由积的自同构群，并刻画这些群何时具有性质FA。这是一项及时的研究，因为最近人们对自由群的自同构群的更强性质T非常感兴趣。

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.