Fundamental groupoids of k-graphs

Details Fundamental groupoids of k-graphs Fundamental groupoids of k-graphs

2004-01-03

arxiv.org/abs/math/0401016v1

Mathematics

Combinatorics

12 pages

Scientific paper

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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