Orbit equivalence of higher-rank graphs

Abstract

We study the notions of continuous orbit equivalence and eventual one-sided conjugacy of finitely-aligned higher-rank graphs and two-sided conjugacy of row-finite higher-rank graphs with finitely many vertices and no sinks or sources. We show that there is a continuous orbit equivalence between two finitely-aligned higher-rank graphs that preserves the periodicity of boundary paths if and only if the boundary path groupoids are isomorphic, and characterise continuous orbit equivalence, eventual one-sided conjugacy, and two-sided conjugacy of higher-rank graphs in terms of the $C^{\ast }$-algebras and the Kumjian-Pask algebras of the higher-rank graphs.

arXiv comment25 pages

References in corpus (8)

• Higher rank graph C*-algebras
• Diagonal-preserving gauge-invariant isomorphisms of graph $C^{\ast }$-algebras
• Reconstruction of groupoids and C*-rigidity of dynamical systems
• Flow equivalence and orbit equivalence for shifts of finite type and isomorphism of their groupoids
• Groupoid models for the C*-algebras of topological higher-rank graphs
• Orbit equivalence of graphs and isomorphism of graph groupoids
• Stability of C*-algebras associated to graphs
• A dynamical characterization of diagonal preserving $\ast$-isomorphisms of graph $C^{\ast }$-algebras