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arXiv · 1705.00439

Bernoulli actions of type III_1 and L^2-cohomology

Stefaan Vaes·Jonas Wahl
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Abstract

We conjecture that a countable group $G$ admits a nonsingular Bernoulli action of type III$_1$ if and only if the first $L^2$-cohomology of $G$ is nonzero. We prove this conjecture for all groups that admit at least one element of infinite order. We also give numerous explicit examples of type III$_1$ Bernoulli actions of the group of integers and the free groups, with different degrees of ergodicity.

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Stefaan Vaes, Jonas Wahl. 2017-05-01. Bernoulli actions of type III_1 and L^2-cohomology. https://arxiv.org/abs/1705.00439

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