arXiv 2201.034092022-01math.OAmath.DS

Classifiability of crossed products by nonamenable groups

Eusebio Gardella, Shirly Geffen, Julian Kranz, Petr Naryshkin

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

英文摘要：

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, $\widetilde{A}_2$-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.

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