Groupoid models for the C*-algebras of topological higher-rank graphs

TL;DR

This paper develops groupoid models for the C*-algebras associated with topological higher-rank graphs, extending existing models to new settings and analyzing their properties such as freeness and amenability.

Contribution

It introduces novel groupoid models for topological higher-rank graph C*-algebras, expanding the theoretical framework and connecting to group crossed products.

Findings

Groupoid models accurately represent Toeplitz and Cuntz-Krieger algebras of topological higher-rank graphs.

The models exhibit essential freeness and amenability under certain conditions.

Results extend the theory of graph algebras and their dynamical systems representations.

Abstract

We provide groupoid models for Toeplitz and Cuntz-Krieger algebras of topological higher-rank graphs. Extending the groupoid models used in the theory of graph algebras and topological dynamical systems to our setting, we prove results on essential freeness and amenability of the groupoids which capture the existing theory, and extend results involving group crossed products of graph algebras.