Related papers: On a quantitative operator K-theory

The equivariant coarse index is well-understood and widely used for actions by discrete groups. We extend the definition of this index to general locally compact groups. We use a suitable notion of admissible modules over $C^*$-algebras of…

These notes cover the contents of three survey lectures held at the ICTP Trieste Summer school on High dimensional manifold theory 2001. They introduce techniques coming from the theory of operator algebras. We will focus on the basic…

It is proved that the K_0-group of a cluster C*-algebra is isomorphic to the corresponding cluster algebra. As a corollary, one gets a shorter proof of the positivity conjecture for cluster algebras. As an example, we consider a cluster…

We consider the construction of twisted tensor products in the category of C*-algebras equipped with orthogonal filtrations and under certain assumptions on the form of the twist compute the corresponding quantum symmetry group, which turns…

Exploiting the graph product structure and results concerning amalgamated free products of C*-algebras we provide an explicit computation of the K-theoretic invariants of right-angled Hecke C*-algebras, including concrete algebraic…

Spielberg's construction of C*-algebras from left cancellative small categories is a common generalization for most C*-algebras one would consider to come from ``combinatorial data,'' including graph and $k$-graph C*-algebras, Li's…

We introduce certain $C^*$-algebras and $k$-graphs associated to $k$ finite dimensional unitary representations $\rho_1,...,\rho_k$ of a compact group $G$. We define a higher rank Doplicher-Roberts algebra $\mathcal{O}_{\rho_1,...,\rho_k}$,…

In this paper, we introduce the quantitative coarse Baum-Connes conjecture with coefficients (or QCBC, for short) for proper metric spaces which refines the coarse Baum-Connes conjecture. And we prove that QCBC is derived by the coarse…

We compute explicitly the K-groups of some boundary groupoid C*-algebras with exponential isotropy subgroups. Then we derive index formulas that computes the K-theoretic and Fredholm indexes of elliptic (respectively totally elliptic)…

We generalise the theory of Cuntz-Krieger families and graph algebras to the class of finitely aligned $k$-graphs. This class contains in particular all row-finite $k$-graphs. The Cuntz-Krieger relations for non-row-finite $k$-graphs look…

We introduce a bivariant version of the Cuntz semigroup as equivalence classes of order zero maps generalizing the ordinary Cuntz semigroup. The theory has many properties formally analogous to KK-theory including a composition product. We…

We prove the existence of a map of spectra $\tau_A \colon kA \to lA$ between connective topological K-theory and connective algebraic L-theory of a complex $C^*$-algebra A which is natural in A and compatible with multiplicative structures.…

We consider a class of C*-algebras associated to one parameter continuous tensor product systems of Hilbert modules, which can be viewed as continuous counterparts of Pimsner's Toeplitz algebras. By exhibiting a homotopy of…

It was shown by Rordam and the second named author that a countable group G admits an action on a compact space such that the crossed product is a Kirchberg algebra if, and only if, G is exact and non-amenable. This construction allows a…

Let $G=K\ltimes A$ be the semi-direct product group of a compact group $K$ acting on an abelian locally compact group $A$. We describe the $C^*$-algebra $C^*(G)$ of $G$ in terms of an algebra of operator fields defined over the spectrum of…

We prove that united K-theory is a surjective functor from the category of real simple purely infinite C*-algebras to the cateogry of countable acyclic CRT-modules.

We compute the genus of a rational quadratic form in terms of the K-theory of a C*-algebra attached to the adelic orthogonal group of the form. As a corollary, one gets a higher composition law for the rational quadratic forms. As an…

We will study some modifications to the notion of an exact C*-algebra by replacing the minimal tensor product with the reduced free product. First we will demonstrate how the reduced free product of a short exact sequence of C*-algebras…

Given a row-finite $k$-graph $\Lambda$ with no sources we investigate the $K$-theory of the higher rank graph $C^*$-algebra, $C^*(\Lambda)$. When $k=2$ we are able to give explicit formulae to calculate the $K$-groups of $C^*(\Lambda)$. The…

Let $A$ be a C*-algebra, $J \subset A$ a C*-subalgebra, and let $B$ be a stable C*-algebra. Under modest assumptions we organize invertible C*-extensions of $A$ by $B$ that are trivial when restricted onto $J$ to become a group…