APERIODICITY CONDITIONS IN TOPOLOGICAL k-GRAPHS

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 improveme...

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Bibliographic Details
Published in:Journal of operator theory 2014-08, Vol.72 (1), p.3-14, Article 3
Main Author: WRIGHT, SARAH E.
Format: Article
Language:English
Subjects:
Algebraic topology
Factorization
Functors
Graph theory
Homeomorphism
Topological compactness
Topological spaces
Topology
Vertices
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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.
ISSN:0379-4024
1841-7744
DOI:10.7900/jot.2012aug20.196