$C^*$-rigidity of dynamical systems and \'etale groupoids

TL;DR

This paper introduces how étale groupoids can be used to establish $C^*$-rigidity results for topological dynamical systems, providing an accessible overview of the topic for a masterclass audience.

Contribution

It offers an introductory perspective on applying étale groupoids to achieve $C^*$-rigidity in dynamical systems, bridging concepts for new researchers.

Findings

Étale groupoids facilitate $C^*$-rigidity proofs.

Provides foundational understanding for future research.

Connects dynamical systems with operator algebra techniques.

Abstract

This is some lecture notes I wrote for the masterclass \emph{Rigidity of $C^*$-algebras associated to dynamics} held at the University of Copenhagen October 16-20, 2017. The notes is attempt to give an introduction to how \'etale groupoids can be used to obtain $C^*$-rigidity result for topological dynamical systems.