"Geometry and Analysis on Groups" Research Seminar
Topological full groups
Leonhard Katzlinger (University of Vienna)
It is a question raised ia by Vershik, for which measure-class preserving group actions on probability spaces the associated Koopman representation is irreducible. The list of actions for which this can be answered affirmatively is rather short. Topological full groups of étale groupoids, a broad survey of which was the aim of my masters thesis, have been having considerable impact on group theory in recent years. In this talk I demonstrate that for a specific class of étale groupoids the Koopman representation of the action of the associated topological full group on the Cantor space is irreducible.