We give a detailed introduction to the theory of Cuntz semigroups for C*-algebras.
Beginning with the most basic definitions and technical lemmas, we present several results …

The Cuntz semigroup of a $ C^* $-algebra is an important invariant in the structure and
classification theory of $ C^* $-algebras. It captures more information than $ K $-theory but is …

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 …

The uncovering of new structure on the Cuntz semigroup of a C*-algebra of stable rank one
leads to several applications: we answer affirmatively, for the class of stable rank-one C …

The Corona Factorization Property, originally invented to study extensions of C*-algebras,
conveys essential information about the intrinsic structure of the C*-algebra. We show that …

For any ring R, we introduce an invariant in the form of a partially ordered abelian
semigroup\({\mathrm S}(R)\) built from an equivalence relation on the class of countably …

We show that abstract Cuntz semigroups form a closed symmetric monoidal category. Thus,
given Cuntz semigroups and, there is another Cuntz semigroup playing the role of …

We investigate the interplay of the following regularity properties for non-simple $\mathrm
C^* $-algebras: finite nuclear dimension, $\mathcal Z $-stability, and algebraic regularity in …

We establish the Borel computability of various C*-algebra invariants, including the Elliott
invariant and the Cuntz semigroup. As applications, we deduce that AF algebras are …

The uncovering of new structure on the Cuntz semigroup of a C*-algebra of stable rank one
leads to several applications: We answer affirmatively, for the class of stable rank one C …