Groups of Automorphisms and Almost Automorphisms of Trees: Subgroups and Dynamics
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.
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I wish to thank the organizers of the program Winter of Disconnectedness which took place in Newcastle, Australia, in 2016, for the invitation to give this series of lectures, and also for the encouragement to make these notes available. I would particularly like to thank Colin Reid and George Willis for welcoming me so warmly. ERC grant #278469 partially supported my participation in this program, and this support is gratefully acknowledged. Finally thanks are due to Ben Brawn for pointing out typos and mistakes in a former version of these notes.
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