Journal of the European Mathematical Society


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Volume 14, Issue 5, 2012, pp. 1513–1518
DOI: 10.4171/JEMS/338

Published online: 2012-08-29

Pairings, duality, amenability and bounded cohomology

Jacek Brodzki[1], Graham A. Niblo[2] and Nick J. Wright[3]

(1) University of Southampton, United Kingdom
(2) University of Southampton, UK
(3) University of Southampton, United Kingdom

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.

Keywords: Amenability, group cohomology, bounded cohomology, uniformly finite homology, invariant means

Brodzki Jacek, Niblo Graham, Wright Nick: Pairings, duality, amenability and bounded cohomology. J. Eur. Math. Soc. 14 (2012), 1513-1518. doi: 10.4171/JEMS/338