Fundamental groupoids of k-graphs

摘要

k-graphs are higher-rank analogues of directed graphs which were firstdeveloped to provide combinatorial models for operator algebras ofCuntz-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 graphcalled the 1-skeleton.We also explore thefailure, in general, of k-graphs to faithfully embed intotheir fundamental groupoids.