Dense totipotent free subgroups of full groups

Abstract: In this talk, we will be interested in measure-preserving actions of countable groups on standard probability spaces, and more precisely in the partitions of the space into orbits that they induce, also called measure-preserving equivalence relations. In 2000, Gaboriau obtained a characterization of the ergodic equivalence relations which come from non-free actions of the free group on $n > 1$ generators: these are exactly the equivalence relations of cost less than n. A natural question is: how non-free can these actions be made, and what does the action on each orbit look like? We will obtain a satisfactory answer by showing that the action on each orbit can be made totipotent, which roughly means "as rich as possible", and furthermore that the free group can be made dense in the ambient full group of the equivalence relation.

This is joint work with Alessandro Carderi and Damien Gaboriau.

group theory

Audience: researchers in the discipline

Symmetry in Newcastle