Related papers: $K$-theory of co-existentially closed continua

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

We use equivariant methods to establish basic properties of orbifold K-theory. We introduce the notion of twisted orbifold K-theory in the presence of discrete torsion, and show how it can be explicitly computed for global quotients.

We construct a sequence of $n-1$ cyclic exact sequences that can be used to compute the $K$-theory of the $C^\star$-algebra crossed product $A \ltimes {\mathbb Z}_n$.

We show that for a coconnective ring spectrum satisfying regularity and flatness assumptions, its algebraic K-theory agrees with that of its $\pi_0$. We prove this as a consequence of a more general devissage result for stable infinity…

In this paper we introduce a new formalism for $K$-theory, called squares $K$-theory. This formalism allows us to simultaneously generalize the usual three-term relation $[B] = [A] + [C]$ for an exact sequence $A \hookrightarrow B…

We show that the K-theory cosheaf is a complete invariant for separable continuous fields with vanishing boundary maps over a finite-dimensional compact metrizable topological space whose fibers are stable Kirchberg algebras with rational…

We introduce an equivariant algebraic kk-theory for G-algebras and G-graded algebras. We study some adjointness theorems related with crossed product, trivial action, induction and restriction. In particular we obtain an algebraic version…

In this article we describe the equivariant and ordinary topological $K$-ring of a toric bundle with fiber a $T$-{\it cellular} toric variety. This generalizes the results in \cite{su} on $K$-theory of smooth projective toric bundles. We…

We show that a sequence is q-holonomic if and only if it satisfies the elimination property for any subset of variables. The same result also holds for holonomic sequences. As an application, we prove several conjectured closure properties…

Following Hopkins and Singer, we give a definition for the differential equivariant K-theory of a smooth manifold acted upon by a finite group. The ring structure for differential equivariant K-theory is developed explicitly. We also…

Using the Baum-Connes conjecture with coefficients, we develop a K-theory formula for reduced C*-algebras of strongly $0$-$E$-unitary inverse semigroups, or equivalently, for certain reduced partial crossed products. In the case of…

KK-theory is a bivariant and homotopy-invariant functor on $C^*$-algebras that combines K-theory and K-homology. KK-groups form the morphisms in a triangulated category. Spanier-Whitehead K-Duality intertwines the homological with the…

We discuss twisted cohomology, not just for ordinary cohomology but also for $K$-theory and other exceptional cohomology theories, and discuss several of the applications of these in mathematical physics. Our list of applications is by no…

This note consists of three unrelated remarks. First, we demonstrate how roughly speaking $*$-homomorphisms between matrix stable $C^*$-algebras are exactly the uniformly continuous $*$-preserving group homomorphisms between their genral…

We give a new proof of the universal property of $KK^G$-theory with respect to stability, homotopy invariance and split-exactness for $G$ a locally compact group, or a locally compact (not necessarily Hausdorff) groupoid, or a countable…

We define a notion of symmetric monoidal closed (SMC) theory, consisting of a SMC signature augmented with equations, and describe the classifying categories of such theories in terms of proof nets.

A noncommutative solenoid is the C*-algebra $C^\ast(\Q_N^2,\sigma)$ where $\Q_N$ is the group of the $N$-adic rationals twisted and $\sigma$ is a multiplier of $\Q_N^2$. In this paper, we use techniques from noncommutative topology to…

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 prove that graded K-theory is universal among oriented Borel-Moore homology theories with a multiplicative periodic formal group law.

Let G be a discrete group. We give methods to compute for a generalized (co-)homology theory its values on the Borel construction (EG x X)/G of a proper G-CW-complex X satisfying certain finiteness conditions. In particular we give formulas…