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arXiv · 1205.2858

Topological realizations and fundamental groups of higher-rank graphs

S. Kaliszewski·Alex Kumjian·John Quigg·Aidan Sims
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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 \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.

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S. Kaliszewski, Alex Kumjian, John Quigg, Aidan Sims. 2012-05-13. Topological realizations and fundamental groups of higher-rank graphs. https://arxiv.org/abs/1205.2858

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