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arXiv · 2201.03409

Classifiability of crossed products by nonamenable groups

Eusebio Gardella·Shirly Geffen·Julian Kranz·Petr Naryshkin
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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, $\widetilde{A}_2$-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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Eusebio Gardella, Shirly Geffen, Julian Kranz, Petr Naryshkin. 2022-01-10. Classifiability of crossed products by nonamenable groups. https://arxiv.org/abs/2201.03409

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