We introduce the notion of a topological higher-rank graph, a unified generalization of the higher-rank graph and the topological graph. Using groupoid techniques, we define the Toeplitz and Cuntz-Krieger algebras of topological higher-rank graphs, and show that the C*-algebras defined are coherent with the existing theory.
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Univ Orleans, Dept Math, BP 6759, F-45067 Orleans 2, France
CNRS, UMR 7349, BP 6759, F-45067 Orleans 2, France
FR 2964, BP 6759, F-45067 Orleans 2, FranceUniv Orleans, Dept Math, BP 6759, F-45067 Orleans 2, France
Renault, Jean
Sims, Aidan
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Univ Wollongong, Sch Math & Appl Stat, Austin Keane Bldg 15, Wollongong, NSW 2522, AustraliaUniv Orleans, Dept Math, BP 6759, F-45067 Orleans 2, France
Sims, Aidan
Williams, Dana P.
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Dartmouth Coll, Dept Math, Hanover, NH 03755 USAUniv Orleans, Dept Math, BP 6759, F-45067 Orleans 2, France
Williams, Dana P.
Yeend, Trent
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Univ Newcastle, Sch Math & Phys Sci, Bldg 5, Callaghan, NSW 2308, AustraliaUniv Orleans, Dept Math, BP 6759, F-45067 Orleans 2, France