Publication Details

Kaliszewski, S., Kumjian, A., Quigg, J. C. & Sims, A. (2015). Topological realizations and fundamental groups of higher-rank graphs. Proceedings of the Edinburgh Mathematical Society, 59 (1), 143-168.


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.

Grant Number

ARC/DP120100389, ARC/FT100100533