Actions and homomorphisms of topological full groups

Vortrag von Dr. Nicolas Matte Bon

Datum: 15.11.17  Zeit: 15.45 - 16.45  Raum: ETH HG G 43

To any group or pseudogroup of homeomorphisms of the Cantor set one can associate a larger (countable) group, called the topological full group. It is a complete invariant of the groupoid of germs of the underlying action (every isomorphism between full groups is implemented by a conjugacy of the corresponding pseudogroups). First I'll discuss a result relating the growth of the orbits of a pseudogroup to a combinatorial fixed point property of its full group, and explain an application related to co-amenability and growth of Schreier graphs of finitely generated groups. Next, I will discuss a theorem on the possible actions on topological full groups on compact spaces, and apply it to show that arbitrary homomorphisms between full groups are often implemented at the level of the groupoids of germs. These results are proven working in the Chabauty space.