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

Lead Research Organisation: University of Southampton
Department Name: Sch of Mathematical Sciences


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.


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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509747/1 01/10/2016 30/09/2021
1949273 Studentship EP/N509747/1 28/09/2017 31/03/2021 Naomi Andrew