  We investigate topological realizations of higher-rank graphs. We show that
the fundamental group of a higher-rank graph coincides with the fundamental
group of its topological realization. We also show that topological realization
of higher-rank graphs is a functor, and that for each higher-rank graph
\Lambda, this functor determines a category equivalence between the category of
coverings of \Lambda\ and the category of coverings of its topological
realization. We discuss how topological realization relates to two standard
constructions for k-graphs: projective limits and crossed products by finitely
generated free abelian groups.
