Pullbacks, [formula omitted]-algebras, and their Cuntz semigroup

Abstract

In this paper we analyse the structure of the Cuntz semigroup of certain C ( X ) -algebras, for compact spaces of low dimension, that have no K 1 -obstruction in their fibres in a strong sense. The techniques developed yield computations of the Cuntz semigroup of some surjective pullbacks of C ⁎ -algebras. As a consequence, this allows us to give a complete description, in terms of semigroup valued lower semicontinuous functions, of the Cuntz semigroup of C ( X , A ) , where A is a not necessarily simple C ⁎ -algebra of stable rank one and vanishing K 1 for each closed, two-sided ideal. We apply our results to study a variety of examples.