# Journal of Operator Theory

Volume 72, Issue 1, Summer 2014 pp. 3-14.

Aperiodicity conditions in topological $k$-graphs

**Authors**:
Sarah E. Wright

**Author institution:** Department of Mathematics and Computer Science,
College of the Holy Cross, Worcester, 01610, U.S.A.

**Summary: **We give two new conditions on topological $k$-graphs
equivalent to 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 $C^*$-algebra.

**DOI: **http://dx.doi.org/10.7900/jot.2012aug20.196

**Keywords: **topological $k$-graph, higher-rank graph, graph algebra,
aperiodicity

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