Classifiability of crossed products by nonamenable groups

Abstract

We show that all amenable, minimal actions of a large class of nonamenable countable groups on compact metric spaces have dynamical comparison. This class includes all nonamenable hyperbolic groups, many HNN-extensions, nonamenable Baumslag-Solitar groups, a large class of amalgamated free products, lattices in many Lie groups, ${\tilde{A}}_2$-groups, as well as direct products of the above with arbitrary countable groups. As a consequence, crossed products by amenable, minimal and topologically free actions of such groups on compact metric spaces are Kirchberg algebras in the UCT class, and are therefore classified by $K$-theory.

v2: 30 pages, 1 figure. To appear in J. Reine Angew. Math. (Crelle)

Cited by in corpus (1)

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