Related papers: An Equivariant K-Theory Functor from Spaces to lam…

Bivariant (equivariant) K-theory is the standard setting for non-commutative topology. We may carry over various techniques from homotopy theory and homological algebra to this setting. Here we do this for some basic notions from…

We construct equivariant $KK$-theory with coefficients in $\mathbb{R}$ and $\mathbb{R}/\mathbb{Z}$ as suitable inductive limits over ${\rm II}_1$-factors. We show that the Kasparov product, together with its usual functorial properties,…

This note gives an overview of the mathematical framework underlying topological insulators, highlighting the connection to K-theory and vector bundles. We see ``real'' and ``quaternionic'' vector bundles arise naturally in the presence of…

Given a group, we construct a fundamental additive functor on its orbit category. We prove that any isomorphism conjecture valid for this fundamental isomorphism functor holds for all additive functors, like K-theory, cyclic homology,…

In the present paper the cyclic homology functor from the category of $A_\infty$-algebras over any commutative unital ring $K$ to the category of graded $K$-modules is constructed. Further, it is showed that this functor sends homotopy…

For a countable group $G$ we construct a small, idempotent complete, symmetric monoidal, stable $\infty$-category $\mathrm{KK}^{G}_{\mathrm{sep}}$ whose homotopy category recovers the triangulated equivariant Kasparov category of separable…

Let $n \geq 2$ be an integer. An \emph{$n$-potent} is an element $e$ of a ring $R$ such that $e^n = e$. In this paper, we study $n$-potents in matrices over $R$ and use them to construct an abelian group $K_0^n(R)$. If $A$ is a complex…

We show that in $K$-theory-like categories many corner embeddings into a discrete algebra of compact operators are invertible, and consequently functors on splitexact algebraic $KK$-theory are faithful if and only if they are faithful on…

We study the algebraic $K$-theory of the ring of continuous functions on a compact Hausdorff space with values in a local division ring, e.g., a local field: We compute its negative $K$-theory and show its $K$-regularity. The complex case…

Let $X(Q,\Lambda)$ be a quasitoric manifold associated to a simple convex polytope $Q$ and characteristic function $\Lambda$. Let $T\cong (\mathbb{S}^1)^n$ denote the compact $n$-torus acting on $X=X(Q,\Lambda)$. The main aim of this…

We introduce an equivariant version of the Cuntz semigroup, that takes an action of a compact group into account. The equivariant Cuntz semigroup is naturally a semimodule over the representation semiring of the given group. Moreover, this…

A kind of unstable homotopy theory on the category of associative rings (without unit) is developed. There are the notions of fibrations, homotopy (in the sense of Karoubi), path spaces, Puppe sequences, etc. One introduces the notion of a…

A covariant functor from the category of the complex tori to the category of the Effros-Shen algebras is constructed. The functor maps isomorphic complex tori to the stably isomorphic Effros-Shen algebras. Our construction is based on the…

We consider the K-theory of the Hilbert scheme of points in the complex plane, which under McKay correspondence is isomorphic to the space of symmetric functions $\Lambda^n$. We prove a formula conjectured by Boissi\`ere for the…

We generalize the construction of reflection functors from classical representation theory of quivers to arbitrary small categories with freely attached sinks or sources. These reflection morphisms are shown to induce equivalences between…

Given a compact manifold X, the set of simple manifold structures on X x \Delta^k relative to the boundary can be viewed as the k-th homotopy group of a space \S^s (X). This space is called the block structure space of X. We study the block…

Equivariant Loday constructions are a means for providing geometric interpretations of equivariant homology theories. They are usually constructed for a simplicial $G$-set and a $G$-Tambara functor. We study situations where -- depending on…

We define united K-theory for real C*-algebras, generalizing Bousfield's topological united K-theory. United K-theory incorporates three functors -- real K-theory, complex K-theory, and self-conjugate K-theory -- and the natural…

The K-theory of a functor may be viewed as a relative version of the K-theory of a ring. In the case of a Galois extension of a number field F/L with rings of integers A/B respectively, this K-theory of the "norm functor" is an extension of…

We construct a covariant functor from the topological torus bundles to the so-called Cuntz-Krieger algebras; the functor maps homeomorphic bundles into the stably isomorphic Cuntz-Krieger algebras. It is shown, that the K-theory of the…