One-Parameter Continuous Fields of Kirchberg Algebras

Abstract

We prove that all unital separable continuous fields of C*-algebras over [0,1] with fibers isomorphic to the Cuntz algebra $${\mathcal{O}}_n \, (2 \leq n \leq \infty)$$ 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 $$d\in \{0,1\}$$ 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.