 

David Pask, John Quigg, and Iain Raeburn
Fundamental groupoids of kgraphs


Published: 
July 30, 2004

Keywords: 
kgraph, directed graph, small category, groupoid, fundamental group 
Subject: 
Primary 05C20, Secondary 14H30, 18D99 


Abstract
kgraphs are higherrank analogues of directed graphs which were first
developed to provide combinatorial models for operator algebras of
CuntzKrieger 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 1skeleton.
We also explore the
failure, in general, of kgraphs to faithfully embed into
their fundamental groupoids.


Acknowledgements
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
davidp@maths.newcastle.edu.au
John Quigg:
Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287, USA
quigg@math.asu.edu
Iain Raeburn:
School of Mathematical and Physical Sciences, University of Newcastle, NSW 2308, Australia
iain@maths.newcastle.edu.au

