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Pairings, duality, amenability and bounded cohomology

Jacek BrodzkiGraham A. NibloNick J. Wright — 2012

Journal of the European Mathematical Society

We give a new perspective on the homological characterizations of amenability given by Johnson & Ringrose in the context of bounded cohomology and by Block & Weinberger in the context of uniformly finite homology. We examine the interaction between their theories and explain the relationship between these characterizations. We apply these ideas to give a new proof of non-vanishing for the bounded cohomology of a free group.

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