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

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.