IUMJ

Title: The Cuntz semigroup of continuous fields

Authors: Ramon Antoine, Joan Bosa and Francesc Perera

Issue: Volume 62 (2013), Issue 4, 1105-1131

Abstract:

In this paper, we describe the Cuntz semigroup of continuous fields of $\mathrm{C}^{*}$-algebras over one-dimensional spaces whose fibers have stable rank one and trivial $K_1$ for each closed, two-sided ideal. This is done in terms of the semigroup of global sections on a certain topological space built out of the Cuntz semigroups of the fibers of the continuous field. Furthermore, when the fibers have real rank zero, and when we take into account the action of the space, our description yields that the Cuntz semigroup is a classifying invariant if and only if the sheaf is also induced by the Murray-von Neumann semigroup.