Piecewise full groups (a.k.a. topological full groups) of Cantor space homeomorphisms are well-known for containing examples of infinite, finitely generated simple groups. In the theory of totally disconnected locally compact groups there is a need for examples that are compactly generated, topologically simple and not discrete. I will report on what one can (and cannot) do with piecewise full groups to obtain such examples. The construction generalises well-known prototypes such as groups of almost automorphisms of trees and commensurators of profinite branch groups.
Based on work with C.D. Reid and D. Robertson.
By Jeremie Brieussel
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