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On the cohomology of Bernoulli actions

Published online by Cambridge University Press:  28 November 2006

SORIN POPA  and
ROMAN SASYK
SORIN POPA
Affiliation:
Mathematics Department, UCLA, Los Angeles, CA 90095-155505, USA (e-mail: popa@math.ucla.edu)
ROMAN SASYK
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907-2067, USA (e-mail: rsasyk@math.purdue.edu)
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Abstract

We prove that if $G$ is a countable, discrete group having infinite normal subgroups with the relative property (T) of Kazhdan–Margulis, then the Bernoulli shift action of $G$ on $\prod_{g \in G} (X_0, \mu_0)_g$, for $(X_{0},\mu_{0})$ an arbitrary non-trivial probability space, has first cohomology group isomorphic to the character group of $G$.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 1 , February 2007 , pp. 241 - 251
Copyright
2006 Cambridge University Press

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