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David Pask, John Quigg, and Iain Raeburn
Fundamental groupoids of k-graphs
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| Published: |
July 30, 2004
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| Keywords: |
k-graph, directed graph, small category, groupoid, fundamental group |
| Subject: |
Primary 05C20, Secondary 14H30, 18D99 |
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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 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.
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| Acknowledgements
This research was supported by grants from the Australian Research Council and the University of Newcastle
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| 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
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