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.
Original language | English (US) |
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Pages (from-to) | 143-168 |
Number of pages | 26 |
Journal | Proceedings of the Edinburgh Mathematical Society |
Volume | 59 |
Issue number | 1 |
DOIs | |
State | Published - Feb 1 2016 |
Keywords
- CW-complex
- covering
- functor
- fundamental group
- k-graph
- projective limit
ASJC Scopus subject areas
- General Mathematics