Related papers: Controlled KK-theory, and a Milnor exact sequence

We discuss the relative K-theory for a $C^{*}$-algebra, $A$, together with a $C^{*}$-subalgebra, $A' \subseteq A$. The relative group is denoted $K_{i}(A';A), i = 0, 1$, and is due to Karoubi. We present a situation of two pairs $A'…

In an earlier paper, the authors introduced partial translation algebras as a generalisation of group C*-algebras. Here we establish an extension of partial translation algebras, which may be viewed as an excision theorem in this context.…

In this paper we identify QD(A,B), the quasidiagonal classes in KK_1(A,B), in terms of K_*(A) and K_*(B), and we use these results in various applications. Here is our central result. Theorem: Suppose that A is in the category of separable…

We interpret certain equivariant Kasparov groups as equivariant representable K-theory groups. We compute these groups via a classifying space and as K-theory groups of suitable sigma-C*-algebras. We also relate equivariant vector bundles…

We introduce a notion of approximate ideal structure for a $C^*$-algebra, and use it as a tool to study $K$-theory groups. The notion is motivated by the classical Mayer-Vietoris sequence, by the theory of nuclear dimension as introduced by…

We define twisted equivariant K-homology groups using geometric cycles. We compare them with approaches using Kasparov KK-Theory and (twisted) group C*-algebras.

We give an algorithm to compute the $K$-groups of the crossed product by the flip automorphism for a nuclear C$^*$-algebra satisfying the UCT.

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.

In this thesis we generalise the six-term exact sequence in graded $KK$-theory obtained in a paper of Kumjian, Pask and Sims (2017) to allow correspondences with non-compact left action. In particular, this allows us to compute the graded…

We introduce a Milnor type $K$-group associated to commutative algebraic groups over a perfect field. It is an additive variant of Somekawa's $K$-group. We show that the $K$-group associated to the additive group and $q$ multiplicative…

Under mild assumptions, we characterise modules with projective resolutions of length n in the target category of filtrated K-theory over a finite topological space in terms of two conditions involving certain Tor-groups. We show that the…

This paper contains computations of the Cuntz semigroup of separable C*-algebras of the form C_0(X,A), where A is a unital, simple, Z-stable ASH algebra. The computations describe the Cuntz semigroup in terms of Murray-von Neumann…

In this paper we refine a version of bivariant $K$-theory developed by Cuntz to define symmetric spectra representing the $KK$-theory of $C^\ast$-categories and discrete groupoid $C^\ast$-algebras. In both cases, the Kasparov product can be…

We introduce filtered algebraic $K$-theory of a ring $R$ relative to a sublattice of ideals. This is done in such a way that filtered algebraic $K$-theory of a Leavitt path algebra relative to the graded ideals is parallel to the gauge…

We study the validity of the Blackadar-Kirchberg conjecture for extensions of separable, nuclear, quasidiagonal $C^*$-algebras that satisfy the UCT. More specifically, we show that the conjecture for the extension has an affirmative answer…

It was recently shown that each C*-algebra generated by a faithful irreducible representation of a finitely generated, torsion free nilpotent group is classified by its ordered K-theory. For the three step nilpotent group $UT(4,\mathbb{Z})$…

We construct a new bivariant theory, that we call $KE$-theory, which is intermediate between the $KK$-theory of G. G. Kasparov, and the $E$-theory of A. Connes and N. Higson. For each pair of separable graded $C^*$-algebras $A$ and $B$,…

We use controlled topology applied to the action of the infinite dihedral group on a partially compactified plane and deduce two consequences for algebraic K-theory. The first is that the family in the K-theoretic Farrell-Jones conjecture…

We give a decomposition of the equivariant Kasparov category for discrete quantum group with torsions. As an outcome, we show that the crossed product by a discrete quantum group in a certain class preserves the UCT. We then show that…

We determine the class of finite T_0-spaces allowing for a universal coefficient theorem computing equivariant KK-theory by filtrated K-theory.