Minimal Følner foliations are amenable

Details Minimal Følner foliations are amenable Minimal Følner foliations are amenable

2010-01-15

arxiv.org/abs/1001.2793v2

Mathematics

Dynamical Systems

Scientific paper

For finitely generated groups, amenability and F{\o}lner properties are equivalent. However, contrary to a widespread idea, Kaimanovich showed that F{\o}lner condition does not imply amenability for discrete measured equivalence relations. In this paper, we exhibit two examples of $C^\infty$ foliations of closed manifolds that are F{\o}lner and non amenable with respect to a finite transverse invariant measure and a transverse invariant volume, respectively. We also prove the equivalence between the two notions when the foliation is minimal, that is all the leaves are dense, giving a positive answer to a question of Kaimanovich. The equivalence is stated with respect to transverse invarian measures or some tangentially smooth measures. The latter include harmonic measures, and in this case the F{\o}lner condition has to be replaced by $\eta$-F{\o}lner (where the usual volume is modified by the modular form $\eta$ of the measure).

Affiliated with

Also associated with

No associations

Rating

Minimal Følner foliations are amenable does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Minimal Følner foliations are amenable, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Minimal Følner foliations are amenable will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-88212