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On the Cohomology of Actions of Groups by Bernoulli Shifts

Sorin Popa·Roman Sasyk
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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 ${\underset g \in G \to Π} (X_0, μ_0)_g$ for $(X_{0},μ_{0})$ an arbitrary probability space, has first cohomology group isomorphic to the character group of $G$.

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Sorin Popa, Roman Sasyk. 2003-12-19. On the Cohomology of Actions of Groups by Bernoulli Shifts. https://arxiv.org/abs/math/0310211

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