Ramon Antoine

COMPLETIONS OF MONOIDS WITH APPLICATIONS TO THE CUNTZ SEMIGROUP

We provide an abstract categorical framework that relates the Cuntz semigroups of the C

Tensor products and regularity properties of Cuntz semigroups

^*

Examples of Armendariz Rings

-algebras

RECOVERING THE ELLIOTT INVARIANT FROM THE CUNTZ SEMIGROUP

A

Inverting Elements in Rigid Monoids

and

Abstract Bivariant Cuntz Semigroups

A\otimes \mathcal{K}

On rigid monoids with right ACC1

. This is done through a certain completion of ordered monoids by adding suprema of countable ascending sequences. Our construction is rather explicit and we show it is functorial and unique up to isomorphism. This approach is used in some applications to compute the stabilized Cuntz semigroup of certain C

Nilpotent elements and Armendariz rings

^*

Pullbacks, C(X)-algebras, and their Cuntz semigroup

-algebras.

Geometric structure of dimension functions of certain continuous fields

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 often more delicate to handle. We systematically study the lattice and category theoretic aspects of Cuntz semigroups. Given a C*-algebra