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.
De Jeremie Brieussel
De Ivan Mitrofanov
De Rostislav Grigorchuk
De Alejandra Garrido
De Dominik Francoeur
De Yair Hartman
De Mikhail Lyubich
De Vadim Kaimanovich
De Anitha Thillaisundaram
De Mikael de la Salle
De Josh Frisch
De Marialaura Noce
De Gérard Ben Arous
