On the Cohomology of Actions of Groups by Bernoulli Shifts

Abstract

We prove that if $G$ is a countable, discrete group having infinite, normal subgroups with the relative property (T), then the Bernoulli shift action of $G$ on $\underset{g}{\in }G\to \Pi (X_0,{\mu }_0{)}_g$ for $(X_0,{\mu }_0)$ an arbitrary probability space, has first cohomology group isomorphic to the character group of $G$.

9 pages; some corrections in Lemma 3.2 (Dec. 18, 2003), 10 pages

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