New York Journal of Mathematics
Volume 10 (2004) 195-207


David Pask, John Quigg, and Iain Raeburn

Fundamental groupoids of k-graphs

Published: July 30, 2004
Keywords: k-graph, directed graph, small category, groupoid, fundamental group
Subject: Primary 05C20, Secondary 14H30, 18D99

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 k-graph, 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.


This research was supported by grants from the Australian Research Council and the University of Newcastle

Author information

David Pask:
School of Mathematical and Physical Sciences, University of Newcastle , NSW 2308, Australia

John Quigg:
Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287, USA

Iain Raeburn:
School of Mathematical and Physical Sciences, University of Newcastle, NSW 2308, Australia