Soficity, amenability, and dynamical entropy

David Kerr, Hanfeng Li

Published 2010-08-08, updated 2010-11-22Version 2

In a previous paper the authors developed an operator-algebraic approach to Lewis Bowen's sofic measure entropy that yields invariants for actions of countable sofic groups by homeomorphisms on a compact metrizable space and by measure-preserving transformations on a standard probability space. We show here that these measure and topological entropy invariants both coincide with their classical counterparts when the acting group is amenable.