Ergodicity and type of nonsingular Bernoulli actions
Artikel i vetenskaplig tidskrift, 2020

We determine the Krieger type of nonsingular Bernoulli actions G curved right arrow Pi(g is an element of G)({0,1},mu(g)). When G is abelian, we do this for arbitrary marginal measures mu(g). We prove in particular that the action is never of type II infinity if G is abelian and not locally finite, answering Krengel's question for G=Z. When G is locally finite, we prove that type II infinity does arise. For arbitrary countable groups, we assume that the marginal measures stay away from 0 and 1. When G has only one end, we prove that the Krieger type is always I, II1 or III1. When G has more than one end, we show that other types always arise. Finally, we solve the conjecture of Vaes and Wahl (Geom Funct Anal 28:518-562, 2018) by proving that a group G admits a Bernoulli action of type III1 if and only if G has nontrivial first L-2-cohomology.


Michael Björklund

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Zemer Kosloff

The Hebrew University Of Jerusalem

Stefaan Vaes

KU Leuven

Inventiones Mathematicae

0020-9910 (ISSN) 1432-1297 (eISSN)

Vol. In Press


Algebra och logik


Matematisk analys



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