DECOMPOSITION RANK OF APPROXIMATELY SUBHOMOGENEOUS C -ALGEBRAS

It is shown that every Jiang-Su stable approximately subhomogeneous C -algebra has nite decomposition rank. Pre- viously, it was not even known that such algebras have nite nu- clear dimension. A key step in the proof is that subhomogeneous C -algebras are locally approximated by a certain class of more tractable subhomogeneous algebras, namely, a non-commutative generalization of the class of cell complexes. The result is applied to show that Jiang-Su stable minimal Z-crossed products have -