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Tree almost automorphism groups Adrien Le Boudec

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Tree almost automorphism groups Adrien Le Boudec

Abstract: Neretin’s group is the group of tree almost automorphisms, i.e. home- omorphisms of the boundary of the tree that are piecewise tree automorphisms.

It is a locally compact totally disconnected group. It naturally contains the auto- morphism group of the tree as well as some Higman-Thompson group. In this talk I will describe some geometric properties of some generalizations of these groups, prove that they are compactly presented and give an upper bound on their Dehn function.

In the introductory part I will talk about trees and their boundaries, automor- phisms of trees, the topology on the automorphism group of a tree.

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