Let G be a group and let KH be homotopy algebraic K-theory. We prove that if G satisfies the rational KH isomorphism conjecture for the group algebra L 1 [G] with coefficients in the algebra of trace-class operators in ...

We relate the Davis-Lück homology with coefficients in Weibel's homotopy K-theory to the equivariant algebraic kk-theory using homotopy theory and adjointness theorems. We express the left hand side of the assembly map for ...

In this paper we address the classification problem for purely infinite simple Leavitt path algebras of finite graphs over a field ℓ. Each graph E has associated a Leavitt path ℓ-algebra L(E). There is an open question ...

The main topic of this thesis consists in Ordinary and Twisted Topological K-Theory. We begin by describing generalized cohomology theories through the Eilenberg-Steenrod Axioms, in order to set Ordinary K-Theory in these ...

We investigate to what extent homotopy invariant, excisive and matrix stable homology theories help one distinguish between the Leavitt path algebras L.E/ and L.F / of graphs E and F over a commutative ground ring `. We ...

We show that if X is a toric scheme over a regular ring containing a field of finite characteristic, then the direct limit of the K-groups of X taken over any infinite sequence of non-trivial dilations is homotopy invariant. ...

Let B be the ring of bounded operators in a complex, separable Hilbert space. For p > 0 consider the Schatten ideal Lp consisting of those operators whose sequence of singular values is p-summable; put S = S p Lp. Let G ...

In [1] we associated an algebra 1.A/ to every bornological algebra A and an ideal IS.A/ C 1.A/ to every symmetric ideal S C `1. We showed that IS.A/ has K-theoretical properties which are similar to those of the usual ...

We use techniques from both real and complex algebraic geometry to study K-theoretic and related invariants of the algebra C(X) of continuous complex-valued functions on a compact Hausdorff topological space X. For example, ...

The nonabelian tensor square GG of a group G was introduced by R. K. Dennis [8] in a search for new homology functors having a close relationship to K-theory and it is based on the work of C. Miller [14]. Subsequently ...