Related papers: K-theory for generalized Lamplighter groups

In this paper we calculate the K-theory of $C^{\ast}$-algebras given by the norm-closures of spaces of bisingular pseudodifferential operators. We obtain results for the \emph{global} bisingular calculus in the flat ($\Rr^{n_1 + n_2}$)…

We continue the study of the effective content of $K$-theory for C*-algebras, with a focus on AF algebras. We show that from a c.e. presentation of an AF algebra it is possible to compute a representation of the algebra as an inductive…

There are many classes of nonsimple graph C*-algebras that are classified by the six-term exact sequence in K-theory. In this paper we consider the range of this invariant and determine which cyclic six-term exact sequences can be obtained…

We announce new methods for using prismatic cohomology to compute the K-groups of $\mathbb{Z}/p^n$ and related rings. We use computer algebra methods to compute these K-groups through a large range in specific cases and also obtain explicit…

We compute the equivariant $K$-theory $K_G^*(G)$ for a simply connected Lie group $G$ (acting on itself by conjugation). We prove that $K_G^*(G)$ is isomorphic to the algebra of Grothendieck differentials on the representation ring. We also…

We generalize a recent result of Clausen: For a number field with integers O, we compute the K-theory of locally compact O-modules. For the rational integers this recovers Clausen's result as a special case. Our method of proof is quite…

In this paper, we give a K-theoretic classification of real ranks zero inductive limits of generalized dimension drop interval algebras.

We give a complete $K$-theoretical description of when an extension of two simple graph $C^{*}$-algebras is again a graph $C^{*}$-algebra.

We develop a generalization of quantitative $K$-theory, which we call controlled $K$-theory. It is powerful enough to study the $K$-theory of crossed product of $C^*$-algebras by action of \'etale groupoids and discrete quantum groups. In…

In this paper we describe the C*-algebras associated to the Baumslag-Solitar groups with the ordering defined by the usual presentations. These are Morita equivalent to the crossed product C*-algebras obtained by letting the group act on…

A covering of k-graphs (in the sense of Pask-Quigg-Raeburn) induces an embedding of universal C*-algebras. We show how to build a (k+1)-graph whose universal algebra encodes this embedding. More generally we show how to realise a direct…

We reveal a correspondence between the homological torsion of the Bianchi groups and new geometric invariants, which are effectively computable thanks to their action on hyperbolic space. We use it to explicitly compute their integral group…

Let $G$ be a locally compact group with cocompact connected component. We prove that the assembly map from the topological $\k$-theory of $G$ to the $\k$-theory of the reduced $C^*$-algebra of $G$ is an isomorphism.

In this paper, we collect some technical results about weights on C*-algebras which are useful in de theory of locally compact quantum groups in the C*-algebra framework. We discuss the extension of a lower semi-continuous weight to a…

Given a simple, acyclic dimension group $G_{0}$ and countable, torsion-free, abelian group $G_{1}$, we construct a minimal, amenable, \'{e}tale equivalence relation $R$ on a Cantor set whose associated groupoid $C^{*}$-algebra, $C^{*}(R)$,…

Suppose that A is a separable C*-algebra and that G_* is a (graded) subgroup of K_*(A). Then there is a natural short exact sequence 0 \to G_* \to K_*(A) \to K_*(A)/G_* \to 0. In this note we demonstrate how to geometrically realize this…

C*-algebras generalizing Cuntz-Krieger algebras can be associated to hyperbolic homeomorphisms of compact metric spaces. They satisfy a non-commutative form of Spanier-Whitehead duality with respect to K-theory. We prove this for the case…

We construct $C^\ast$-categories that are anologues of the categories used in controlled algebraic $K$-theory. We then show that the reduced $C^\ast$-algebra of a finitely presented group and an associated controlled $C^\ast$-category have…

We study semigroup C*-algebras of semigroups associated with number fields and initial data arising naturally from class field theory. Using K-theoretic invariants, we investigate how much information about the initial number-theoretic data…

We describe a construction by G\'abor Elek, associating C*-algebras with uniformly recurrent subgroups, in the language of groupoid C*-algebras. This allows us to simplify several proofs in the original paper and fully characterise their…