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Bernoulli actions of type III_1 and L^2-cohomology

Tijdschriftbijdrage - Tijdschriftartikel

© 2018, Springer International Publishing AG, part of Springer Nature. We conjecture that a countable group G admits a nonsingular Bernoulli action of type III1 if and only if the first L2-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 III1 Bernoulli actions of the groups Z and the free groups Fn, with different degrees of ergodicity.
Tijdschrift: Geometric and Functional Analysis Gafa
ISSN: 1016-443X
Issue: 2
Volume: 28
Pagina's: 518 - 562
Jaar van publicatie:2018
BOF-keylabel:ja
IOF-keylabel:ja
BOF-publication weight:6
CSS-citation score:2
Authors from:Higher Education
Toegankelijkheid:Open