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Tree almost automorphism groups: elements and subgroups

Banff International Research Station for Mathematical Innovation and Discovery

(Joint work with A. Le Boudec) We begin by giving a detailed overview of the tree almost automorphism groups and describing their relationship to Higman-Thompson groups and topological full groups. We then show each almost automorphism has one of two possible types, corresponding to the dynamics of the action on the boundary. We next consider the subgroups such that every element is contained in a compact subgroup; such groups are the topological analogue of torsion subgroups. We characterize these subgroups in terms of the dynamics of their action on the boundary and deduce that they are indeed locally elliptic - i.e. every finite set is contained in a compact subgroup. We finally consider the commensurated subgroups of almost automorphism groups; these subgroups generalize normal subgroups. We show every commensurated closed subgroup of an almost automorphism group is either finite, compact and open, or equal to the entire group.

Mathematics; Topological groups, lie groups; Abstract harmonic analysis

video/mp4

Author affiliation: Binghamton University

2017-12-11

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63884

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/