One-Parameter Continuous Fields of Kirchberg Algebras

We prove that all unital separable continuous fields of C*-algebras over 0,1] with fibers isomorphic to the Cuntz algebra are trivial. More generally, we show that if A is a separable, unital or stable, continuous field over 0,1] of Kirchberg C*-algebras satisfying the UCT and having finitely generated K-theory groups, then A is isomorphic to a trivial field if and only if the associated K-theory presheaf is trivial. For fixed we also show that, under the additional assumption that the fibers have torsion free K _d -group and trivial K _d+1-group, the K _d -sheaf is a complete invariant for separable stable continuous fields of Kirchberg algebras. M.D. was supported in part by NSF Grant #DMS-0500693. G.A.E. held a Discovery Grant from NSERC Canada.