Article contents
Topological realizations and fundamental groups of higher-rank graphs
Published online by Cambridge University Press: 10 June 2015
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.
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 1 , February 2016 , pp. 143 - 168
- Copyright
- Copyright © Edinburgh Mathematical Society 2016
References
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