Related papers: KK-theory of C*-categories and the analytic assemb…

We compute K-theory for ring C*-algebras in the case of higher roots of unity and thereby completely determine the K-theory for ring C*-algebras attached to rings of integers in arbitrary number fields.

For a separable $C^*$-algebra $A$, we introduce an exact $C^*$-category called the Paschke Category of $A$, which is completely functorial in $A$, and show that its K-theory groups are isomorphic to the topological K-homology groups of the…

We initiate the study of real $C^*$-algebras associated to higher-rank graphs $\Lambda$, with a focus on their $K$-theory. Following Kasparov and Evans, we identify a spectral sequence which computes the $\mathcal{CR}$ $K$-theory of…

We review the recent construction of semifinite spectral triples for graph C^*-algebras. These examples have inspired many other developments and we review some of these such as the relation between the semifinite index and the Kasparov…

We give a description of the value of a finitary localizing invariant, such as algebraic $K$-theory, on the category of sheaves on a locally coherent space $X$. This in particular includes all spaces that arise as spectra of commutative…

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 introduce and investigate some examples of C$^*$-algebras which are related to multiplication maps in the ring of $p$-adic integers. We find ideals within these algebras and use the corresponding short exact sequences to compute the…

Let X be a space, intended as a possibly curved spacetime, and A a precosheaf of C*-algebras on X. Motivated by algebraic quantum field theory, we study the Kasparov and Theta-summable K-homology of A interpreting them in terms of the…

This paper provides a full controlled version of algebraic $K$-theory. This includes a rich array of assembly maps; the controlled assembly isomorphism theorem identifying the controlled group with homology; and the stability theorem…

We compute the Balmer spectrum of the equivariant bootstrap category of separable $G$-C*-algebras when $G$ is a group of prime order.

We consider a construction of C*-algebras from continuous piecewise monotone maps on the circle which generalizes the crossed product construction for homeomorphisms and more generally the construction of Renault, Deaconu and…

Given a completely rational conformal net A on the circle, its fusion ring acts faithfully on the K_0-group of a certain universal C*-algebra associated to A, as shown in a previous paper. We prove here that this action can actually be…

We describe proper correspondences from graph C*-algebras to arbitrary C*-algebras by K-theoretic data. If the target C*-algebra is a graph C*-algebra as well, we may lift an isomorphism on a certain invariant to correspondences back and…

We use the Cayley transform to provide an explicit isomorphism at the level of cycles from van Daele $K$-theory to $KK$-theory for graded $C^*$-algebras with a real structure. Isomorphisms between $KK$-theory and complex or real $K$-theory…

We study the $K$-theory and Swan theory of the group ring $R[G]$, when $G$ is a finite group and $R$ is any ring or ring spectrum. In this setting, the well-known assembly map for $K(R[G])$ has a companion called the coassembly map. We…

We show that unital simple C*-algebras with tracial topological rank zero which are locally approximated by subhomogeneous C^-algebras can be classified by their ordered $K$-theory. We apply this classification result to show that certain…

Strongly self-absorbing $\mathrm{C}^*$-algebras play a distinguished role in the classification of nuclear $\mathrm{C}^*$-algebras. Their dynamical analogues were introduced and extensively studied by Szab\'o. In this paper, we propose a…

Recall that the definition of the $K$-theory of an object C (e.g., a ring or a space) has the following pattern. One first associates to the object C a category A_C that has a suitable structure (exact, Waldhausen, symmetric monoidal, ...).…

We compute K-theory for the reduced group C*-algebras of generalized Lamplighter groups.

We study the noncommutative topology of the $C^*$-algebras $C(\mathbb{C}P_q^{n})$ of the quantum projective spaces within the framework of Kasparov's bivariant K-theory. In particular, we construct an explicit KK-equivalence with the…