Invariant expectations and vanishing of bounded cohomology for exact groups

Details Invariant expectations and vanishing of bounded cohomology for exact groups Invariant expectations and vanishing of bounded cohomology for exact groups

2010-01-05

arxiv.org/abs/1001.0718v5

J. Topol. Anal. 3 (2011), no. 1, 89--107

Mathematics

Functional Analysis

Final version, to appear in the Journal of Topology and Analysis

Scientific paper

10.1142/S1793525311000489

We study exactness of groups and establish a characterization of exact groups in terms of the existence of a continuous linear operator, called an invariant expectation, whose properties make it a weak counterpart of an invariant mean on a group. We apply this operator to show that exactness of a finitely generated group $G$ implies the vanishing of the bounded cohomology of $G$ with coefficients in a new class of modules, which are defined using the Hopf algebra structure of $\ell_1(G)$.

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