Nora Szoke: (Non-)Amenability of topological full groups

Speaker: Nora Szoke

Title:  (Non-)Amenability of topological full groups

Abstract: Juschenko and Monod proved that the topological full group of a minimal Cantor Z-action is always amenable. This provided the first examples of finitely generated (infinite) amenable simple groups. Grigorchuk and Medynets asked if this is true for minimal actions of other amenable groups. Elek and Monod constructed a minimal action of Z^2 for which the topological full group contains a non-abelian free group. We can try to determine all groups G for which the topological full group of a minimal Cantor G-action is always amenable. We will discuss some results in this topic.