Related papers: The coarse Baum--Connes conjecture and groupoids I…

Let F be a global field, A its ring of adeles, G a reductive group over F. We prove the Baum-Connes conjecture for the adelic group G(A).

Geometric property (T) was defined by Willett and Yu, first for sequences of graphs and later for more general discrete spaces. Increasing sequences of graphs with geometric property (T) are expanders, and they are examples of coarse spaces…

We give a definition of differentiable cohomology of a Lie group G (possibly infinite-dimensional) with coefficients in any abelian Lie group. This differentiable cohomology maps both to the cohomology of the group made discrete and to Lie…

This paper continues the author's program to investigate the question of when a homotopy of 2-cocycles $\Omega = \{\omega_t\}_{t \in [0,1]}$ on a locally compact Hausdorff groupoid $\mathcal{G}$ induces an isomorphism of the $K$-theory…

In this paper, we prove the K- and L-theoretical Isomorphism Conjecture for Baumslag-Solitar groups with coefficients in an additive category.

In this paper, the second of a series of two, we continue the study of higher index theory for expanders. We prove that if a sequence of graphs has girth tending to infinity, then the maximal coarse Baum-Connes assembly map is an…

We begin a coarse geometric study of Hilbert geometry. Actually we give a necessary and sufficient condition for the natural boundary of a Hilbert geometry to be a corona, which is a nice boundary in coarse geometry. In addition, we show…

The Baum-Connes assembly map with coefficients $e_{\ast}$ and the Mishchenko-Kasparov assembly map with coefficients $\mu_{\ast}$ are two homomorphisms from the equivariant $K$-homology of classifying spaces of groups to the $K$-theory of…

We describe a geometric counterpart of the Baum-Connes map for the p-adic group GL(n).

A monoid is said to be special if it admits a presentation in which all defining relations are of the form $w = 1$. Groups are familiar examples of special monoids. This article studies the geometric and structural properties of the Cayley…

For every strong coarse homology theory we construct a coarse assembly map as a natural transformation between coarse homology theories. We provide various conditions implying that this assembly map is an equivalence. These results…

Alternative titles of this paper would have been `Index theory without index' or `The Baum-Connes conjecture without Baum.' In 1989, Rieffel introduced an analytic version of deformation quantization based on the use of continuous fields of…

The aim of this review paper is to explain the relevance of Lie groupoids and Lie algebroids to both physicists and noncommutative geometers. Groupoids generalize groups, spaces, group actions, and equivalence relations. This last aspect…

We study the connection between the Baum-Connes conjecture for an ample groupoid $G$ with coefficient $A$ and the K\"unneth formula for the K-theory of tensor products by the crossed product $A\rtimes_r G$. To do so we develop the machinery…

Between the category of exact metric spaces with bounded geometry (about which much is known) and the larger category of arbitrary exact metric spaces (about which little is known) lies the intermediate category of asymptotically exact…

We prove an $\ell^p$-version of the coarse Baum-Connes conjecture for spaces that coarsely embedds into $\ell^q$-spaces for any $p$ and $q$ in $[1,\infty)$.

We establish the Hasse principle (local-global principle) in the context of the Baum-Connes conjecture with coefficients. We illustrate this principle with the discrete group $GL(2,F)$ where $F$ is any global field.

A Hom-group G is a nonassociative version of a group where associativity, invertibility, and unitality are twisted by a map \alpha: G\longrightarrow G. Introducing the Hom-group algebra KG, we observe that Hom-groups are providing examples…

We prove the (generalized) coherence conjecture of Pappas and Rapoport. As a corollary, one theorem of Pappas an Rapoport, which describes the geometry of the special fibers of the local models for ramified unitary groups, holds…

In this monograph we lay the foundation for a theory of coarse groups and coarse actions. Coarse groups are group objects in the category of coarse spaces, and can be thought of as sets with operations that satisfy the group axioms "up to…