Topological realizations and fundamental groups of higher-rank graphs. Issue 1 (10th June 2015) - Kaliszewski, S.; Kumjian, Alex; Quigg, John; Sims, Aidan
Abstract: 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 Λ, this functor determines a category equivalence between the category of coverings of Λ 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.