Orbit equivalence of graphs and isomorphism of graph groupoids

• Toke Meier Carlsen ^[1] ; Marius Lie Winger ^[2]
  1. [1] University of the Faroe Islands

     University of the Faroe Islands

     Islas Feroe

     
  2. [2] Norwegian University of Science and Technology

     Norwegian University of Science and Technology

     Noruega

     
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 123, Nº 2, 2018, págs. 239-248
• Idioma: inglés
• DOI: 10.7146/math.scand.a-105087
• Texto completo no disponible (Saber más ...)
• Resumen

  • We show that the groupoids of two directed graphs are isomorphic if and only if the two graphs are orbit equivalent by an orbit equivalence that preserves isolated eventually periodic points. We also give a complete description of the (topological) isolated points of the boundary path space of a graph. As a result, we are able to show that the groupoids of two directed graphs with finitely many vertices and no sinks are isomorphic if and only if the two graphs are orbit equivalent, and that the groupoids of the stabilisations of two such graphs are isomorphic if and only if the stabilisations of the graphs are orbit equivalent.