Bernoulli actions of type III and L^2-cohomology

Stefaan Vaes
KU Leuven

I present a joint work with Jonas Wahl proving the following result: in most cases, a countable group G admits a Bernoulli action of type III in the sense of Murray and von Neumann if and only if the first L^2-cohomology of G is nonzero. I also present numerous explicit examples of type III_1 Bernoulli actions of the group of integers and of the free groups, with different degrees of ergodicity.

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