Decomposition rank of 𝒵-stable C∗-algebras

We show that C -algebras of the form C.X / ˝ᐆ, where X is compact and Hausdorff and ᐆ denotes the Jiang-Su algebra, have decomposition rank at most 2.This amounts to a dimension reduction result for C -bundles with sufficiently regular fibres.It establishes an important case of a conjecture on the fine structure of nuclear C -algebras of Toms and Winter, even in a nonsimple setting, and gives evidence that the topological dimension of noncommutative spaces is governed by fibres rather than base spaces.Both authors were supported by