On the Cohomology of Actions of Groups by Bernoulli Shifts
Abstract
Description
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 $G$.
9 pages; some corrections in Lemma 3.2 (Dec. 18, 2003), 10 pages
9 pages; some corrections in Lemma 3.2 (Dec. 18, 2003), 10 pages