Aperiodicity Conditions in Topological $k$-Graphs

Abstract

We give two new conditions on topological $k$-graphs that are equivalent to the Yeend's aperiodicity Condition (A). Each of the new conditions concerns finite paths rather than infinite. We use a specific example, resulting from a new construction of a twisted topological $k$-graph, to demonstrate the improvements achieved by the new conditions. Reducing this proof of equivalence to the discrete case also gives a new direct proof of the corresponding conditions in discrete $k$-graphs, where previous proofs depended on simplicity of the corresponding C${}^{\ast }$-algebra.

12 pages, 3 figures, in version 2 the statement of the third condition has been corrected

References in corpus (2)

• Uniqueness theorems for topological higher-rank graph C*-algebras
• When is the Cuntz-Krieger algebra of a higher-rank graph approximately finite-dimensional?

Cited by in corpus (1)

• When is the Cuntz-Krieger algebra of a higher-rank graph approximately finite-dimensional?