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Amenable actions, invariant means and bounded cohomology

By Jacek Brodzki, Graham A. Niblo, Piotr Nowak and Nick Wright

Abstract

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

Topics: QA
Year: 2012
OAI identifier: oai:eprints.soton.ac.uk:143057
Provided by: e-Prints Soton

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Citations

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