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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Graham A. Niblo, Jacek Brodzki, Nick Wright, Pairings, duality, amenability and bounded cohomology. J. Eur. Math. Soc. 14 (2012), no. 5, pp. 1513–1518DOI 10.4171/JEMS/338