Amenable actions, invariant means and bounded cohomology

Details Amenable actions, invariant means and bounded cohomology Amenable actions, invariant means and bounded cohomology

2010-04-02

arxiv.org/abs/1004.0295v1

Mathematics

Group Theory

Scientific paper

We show that topological amenability of an action of a countable discrete group on a compact space is equivalent to the existence of an invariant mean for the action. We prove also that this is equivalent to vanishing of bounded cohomology for a class of Banach G-modules associated to the action, as well as to vanishing of a specific cohomology class. In the case when the compact space is a point our result reduces to a classic theorem of B.E. Johnson characterising amenability of groups. In the case when the compact space is the Stone-\v{C}ech compactification of the group we obtain a cohomological characterisation of exactness for the group, answering a question of Higson.

Affiliated with

Also associated with

No associations

Rating

Amenable actions, invariant means and bounded cohomology 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 Amenable actions, invariant means and bounded cohomology, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Amenable actions, invariant means and bounded cohomology will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-407548