Every finitely generated group is weakly exact

Details Every finitely generated group is weakly exact Every finitely generated group is weakly exact

2011-09-01

arxiv.org/abs/1109.0313v1

Mathematics

Functional Analysis

To appear in the Journal of Functional Analysis

Scientific paper

We show that every finitely generated group admits weak analogues of an invariant expectation, whose existence characterizes exact groups. This fact has a number of applications. We show that Hopf $G$-modules are relatively injective, which implies that bounded cohomology groups with coefficients in all Hopf $G$-modules vanish in all positive degrees. We also prove a general fixed point theorem for actions of finitely generated groups on $\ell_{\infty}$-type spaces. Finally, we define the notion of weak exactness for certain Banach algebras.

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