Related papers: A note on the real coarse Baum-Connes conjecture

Using an equivariant version of Connes' Thom Isomorphism,w}e prove that equivariant $K$-theory is invariant under strict deformation quantization for a compact Lie group action.

This is a survey paper which gathers some results related with the study of Positive Scalar Curvature metrics in connection with the Baum-Connes assembly map.

The additivity theorem for derivateurs associated to complicial biWaldhausen categories is proved. Also, to any exact category in the sense of Quillen a K-theory space is associated. This K-theory is shown to satisfy the additivity,…

The assumptions needed to prove Cox's Theorem are discussed and examined. Various sets of assumptions under which a Cox-style theorem can be proved are provided, although all are rather strong and, arguably, not natural.

For any subfield K of the complex numbers which is not contained in an imaginary quadratic number field, we construct conjugate varieties whose algebras of K-rational (p,p)-classes are not isomorphic. This compares to the Hodge conjecture…

This short note summarizes a number of facts about the ring $K^0(X)$ for $X$ a $4$-dimensional CW-complex. Unusual features of this dimension are that every complex vector bundle is determined up to stable isomorphism by its Chern classes,…

A generalization of Connes-Thom isomorphism is given for stable, homotopy invariant, and split exact functors on separable $C^*$-algebras. As examples of these functors, we concentrate on asymptotic and local cyclic cohomology and the…

We give a survey on the homotopy theory of the regular group of Banach algebras with emphasis on the unstable K-Theory of real and complex C*-algebras

We prove that the Farrell-Jones assembly map for connective algebraic K-theory is rationally injective, under mild homological finiteness conditions on the group and assuming that a weak version of the Leopoldt-Schneider conjecture holds…

We prove the existence of complexified real arrangements with the same combinatorics but different embeddings in the complex projective plane. Such pair of arrangements has an additional property: they admit conjugated equations on the ring…

Let P be a semigroup that admits an embedding into a group G. Assume that the embedding satisfies a certain Toeplitz condition and that the Baum-Connes conjecture holds for G. We prove a formula describing the K- theory of the reduced…

The purpose of this short paper is to investigate relations between various real K-theories. In particular, we show how a real projective bundle theorem implies an unexpected relation between Atiyah's KR-theory and the usual equivariant…

Given C$^*$-algebras $A$ and $B$ and a $^*$-homomorphism $\phi:A\rightarrow B$, we adopt the portrait of the relative $K$-theory $K_*(\phi)$ due to Karoubi using Banach categories and Banach functors. We show that the elements of the…

We compare the domain of the assembly map in algebraic K-theory with respect to the family of finite subgroups with the domain of the assembly map with respect to the family of virtually cyclic subgroups and prove that the former is a…

We investigate when Isomorphism Conjectures, such as the ones due to Baum-Connes, Bost and Farrell-Jones, are stable under colimits of groups over directed sets (with not necessarily injective structure maps). We show in particular that…

In a very celebrated paper A. Connes has formulated a conjecture which is now one of the most important open problem in Operator Algebras. This importance comes from the works of many mathematicians who have found some unexpected equivalent…

We identify a number of decidable and undecidable fragments of first-order concatenation theory. We also give a purely universal axiomatization which is complete for the fragments we identify. Furthermore, we prove some normal-form results.

We introduce a natural map from the space of pure-type complex differential forms on a complex manifold to the corresponding one on the infinitesimal deformations of this complex manifold. By use of this map, we generalize an extension…

We give the details of the construction of a map to restate a conjectural expression about adjoint group action on generic representations in L-packets. We give an application of the construction to give another proof of the classification…

Commutative K-theory, a cohomology theory built from spaces of commuting matrices, has been explored in recent work of Adem, G\'{o}mez, Gritschacher, Lind, and Tillman. In this article, we use unstable methods to construct explicit…