Fundamental groupoids of k-graphs

David Pask, John Quigg, Iain Raeburn

Research output: Contribution to journalReview articlepeer-review

13 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)195-207
Number of pages13
JournalNew York Journal of Mathematics
StatePublished - Jul 30 2004


  • Directed graph
  • Fundamental group
  • Groupoid
  • Small category
  • k-graph

ASJC Scopus subject areas

  • General Mathematics


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