Minimal Følner foliations are amenable

Ana Rechtman

In this talk we will discuss the relation between amenable foliations and foliations with Følner leaves. Both notions are motivated by the corresponding ones on finitely generated groups, and in this context they are equivalent. In contrast, for foliations there are examples of non-amenable foliations with all its leaves Følner. We will begin by discussing the definitions and an example of a non-amenable foliation with Følner leaves. After, we will show that for minimal foliations the two notions are equivalent: a minimal foliation with (almost all) its leaves Følner is amenable. The equivalence is stated for foliations equipped with a transverse invariant measure or with a harmonic measure.