Fundamental groupoids of k-graphs

Authors

David A. Pask, University of WollongongFollow
Iain F. RaeburnFollow
John C. Quigg, University of Arizona

RIS ID

17458

Publication Details

Pask, D. A., Quigg, J. C. & Raeburn, I. F. (2004). Fundamental groupoids of k-graphs. The New York Journal of Mathematics, 10 195-207.

Abstract

k-graphs are higher-rank analogues of directed graphs which were first developed to provide combinatorial models for operator algebras of Cuntz– Krieger type. Here we develop a theory of the fundamental groupoid of a kgraph, and relate it to the fundamental groupoid of an associated graph called the 1-skeleton. We also explore the failure, in general, of k-graphs to faithfully embed into their fundamental groupoids.