K-theory and homotopies of 2-cocycles on higher-rank graphs

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Abstract

This paper continues our investigation into the question of when a homotopy of 2-cocycles on a locally compact Hausdorff groupoid gives rise to an isomorphism of the K-theory groups of the twisted groupoid C*-algebras. Our main result, which builds on work by Kumjian, Pask, and Sims, shows that a homotopy of 2-cocycles on a row-finite higher-rank graph 3 gives rise to twisted groupoid C*-algebras with isomorphic K-theory groups. (The groupoid in question is the path groupoid of 3.) We also establish a technical result: any homotopy of 2-cocycles on a locally compact Hausdorff groupoid G gives rise to an upper semicontinuous bundle of C*-algebras.

Original languageEnglish
Pages (from-to)407-426
Number of pages20
JournalPacific Journal of Mathematics
Volume278
Issue number2
DOIs
StatePublished - 2015

Keywords

  • 2-cocycle
  • C (X)-algebra
  • Groupoid
  • Higher-rank graph
  • K-theory
  • Twisted groupoid C*-algebra
  • Twisted k-graph C*-algebra
  • Upper semicontinuous C*-bundle

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