Topological Realizations and Fundamental Groups of Higher-Rank Graphs

Steven Kaliszewski, Alex Kumjian, John Quigg, Aidan Sims

Research output: Contribution to journalArticle

3 Citations (Scopus)

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)
JournalProceedings of the Edinburgh Mathematical Society
DOIs
StateAccepted/In press - Jun 10 2015

Fingerprint

Fundamental Group
Graph in graph theory
Functor
Covering
Projective Limit
Crossed Product
Free Group
Finitely Generated
Abelian group
Equivalence

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Topological Realizations and Fundamental Groups of Higher-Rank Graphs. / Kaliszewski, Steven; Kumjian, Alex; Quigg, John; Sims, Aidan.

In: Proceedings of the Edinburgh Mathematical Society, 10.06.2015.

Research output: Contribution to journalArticle

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