Title: Transitivity degree and non-free actions on the circle
Abstract: The transitivity degree of a group \(G\) is an invariant of \(G\) associated to representations of \(G\) as a permutation group: this is the largest integer \(k\) such that \(G\) admits a faithful \(k\)-transitive action; and if there is no such integer then the transitivity degree is infinite.
For several classes of groups coming from geometric group theory, this invariant is known to be infinite, notably by a result of Hull--Osin. Recently
Gelander--Glasner--Soifer showed that the same holds for Zariski dense subgroups of \(SL(2,K)\), where \(K\) is a local field.
In the talk we will discuss the situation of certain groups coming from ``dynamical group theory". For example for groups \(G\) having a minimal and non-free action on the circle by homeomorphisms, we will see that the transitivity degree can be explicitly computed, and is determined by the action of \(G\) on its orbits on the circle. This is joint work with Nicolas Matte Bon.
Pierre-Emmanuel Caprace
