Classifiability of crossed products by nonamenable groups

Eusebio Gardella, Shirly Geffen, Julian Kranz, Petr Naryshkin

Research output: Contribution to journalArticlepeer-review


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, A2-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.

Original languageEnglish
Pages (from-to)285-312
Number of pages28
JournalJournal fur die Reine und Angewandte Mathematik
Issue number797
StatePublished - 1 Apr 2023
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


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