Topological realizations and fundamental groups of higher-rank graphs

Steven Kaliszewski, Alex Kumjian, John Quigg, Aidan Sims

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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 languageEnglish (US)
Pages (from-to)143-168
Number of pages26
JournalProceedings of the Edinburgh Mathematical Society
Volume59
Issue number1
DOIs
StatePublished - Feb 1 2016

Keywords

  • CW-complex
  • covering
  • functor
  • fundamental group
  • k-graph
  • projective limit

ASJC Scopus subject areas

  • Mathematics(all)

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