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}
}
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… 

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