Classification of inductive limits of 1-dimensional NCCW complexes

A classification result is obtained for the C∗-algebras that are (stably isomorphic to) inductive limits of 1-dimensional noncommutative CW complexes with trivial K1-group. The classifying functor Cu∼ is defined in terms of the Cuntz semigroup of the unitization of the algebra. For the simple C∗-algebras covered by the classification, Cu∼ reduces to the ordered K0-group, the cone of traces, and the pairing between them. As an application of the classification, it is shown that the crossed products by a quasi-free action O2⋊λRO2⋊λR are all isomorphic for a dense set of positive irrational numbers λλ.