We investigate the K-theory of twisted higher-rank-graph algebras by adapting
parts of Elliott's computation of the K-theory of the rotation algebras. We
show that each 2-cocycle on a higher-rank graph taking values in an abelian
group determines a continuous bundle of twisted higher-rank graph algebras over
the dual group. We use this to show that for a circle-valued 2-cocycle on a
higher-rank graph obtained by exponentiating a real-valued cocycle, the
K-theory of the twisted higher-rank graph algebra coincides with that of the
untwisted one.Comment: 15 pages; four diagrams prepared in Tik
