Soficity, amenability, and dynamical entropy

Abstract

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.

Locations

• arXiv (Cornell University) - View - PDF
• American Journal of Mathematics - View
• CiteSeer X (The Pennsylvania State University) - View - PDF