These are notes of a lecture series delivered during the program Winter of Disconnectedness in Newcastle, Australia, 2016. The exposition is on several families of groups acting on trees by automorphisms or almost automorphisms, such as Neretin’s groups, Thompson’s groups, and groups acting on trees with almost prescribed local action. These include countable discrete groups as well as locally compact groups. The focus is on the study of certain subgroups, e.g. finite covolume subgroups, or subgroups satisfying certain normality conditions, such as commensurated subgroups or uniformly recurrent subgroups.
Le Boudec, A. (2018). Groups of automorphisms and almost automorphisms of trees: subgroups and dynamics. 2016 MATRIX Annals, np(np), 501-523. https://doi.org/10.1007/978-3-319-72299-3_22 (Original work published 2018)