  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 the theory of covering spaces for k-graphs,
obtaining a satisfactory version of the usual topological classification in
terms of subgroups of a fundamental group. We then use this classification to
describe the C*-algebras of covering k-graphs as crossed products by coactions
of homogeneous spaces, generalizing recent results on the C*-algebras of
graphs.
