• DOI:10.1017/S0013091515000061
• Corpus ID: 52360175

Topological realizations and fundamental groups of higher-rank graphs

@article{Kaliszewski2012TopologicalRA,
  title={Topological realizations and fundamental groups of higher-rank graphs},
  author={S. Kaliszewski and Alex Kumjian and John Quigg and Aidan Sims},
  journal={Proceedings of the Edinburgh Mathematical Society},
  year={2012},
  volume={59},
  pages={143 - 168}
}

• S. Kaliszewski, A. Kumjian, +1 author A. Sims
• Published 13 May 2012
• Mathematics
• Proceedings of the Edinburgh Mathematical Society

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.