Related papers: The Baum-Connes conjecture for extensions

A proof of Thompson's conjecture for real semi-simple Lie groups has been given by Kapovich, Millson, and Leeb. In this note, we give another proof of the conjecture by using a theorem of Alekseev, Meinrenken, and Woodward from symplectic…

We construct a Baum--Connes assembly map localised at the unit element of a discrete group $\Gamma$. This morphism, called $\mu_\tau$, is defined in $KK$-theory with coefficients in $\mathbb{R}$ by means of the action of the projection…

We show that the classical Baum-Connes assembly map is quantitatively an isomorphism for a class of lacunary hyperbolic groups, and we explain how to see that this class contains many examples of groups that contain graph sequences of large…

In their study of the Yamabe problem in the presence of isometry group, Hebey and Vaugon announced a conjecture. This conjecture generalizes Aubin's conjecture, which has already been proven and is sufficient to solve the Yamabe problem. In…

Cohen, Lenstra, and Martinet have given conjectures for the distribution of class groups of extensions of number fields, but Achter and Malle have given theoretical and numerical evidence that these conjectures are wrong regarding the Sylow…

We show that the Farrell-Jones Conjecture holds for fundamental groups of graphs of groups with abelian vertex groups. As a special case, this shows that the conjecture holds for generalized Baumslag-Solitar groups.

In this paper we prove the Aubert-Baum-Plymen-Solleveld conjecture for the split classical groups and establish the connection with the Langlands correspondence. To do this, we review the notion of cuspidality for enhanced Langlands…

We give a generalization and a short mechanized proof of determinant conjectured by G. Kuperberg and J. Propp. Further generalizations and applications of the method to some q-analogues may be found in http://www.math.temple.edu/~tewodros

We study a going-down principle for {\'e}tale groupoids and its applications, extending the earlier results for locally compact groups by Chabert, Echterhoff and Oyono-Oyono, and for ample groupoids by B{\"o}nicke and by…

We prove an extension of the Moore-Schmidt theorem on the triviality of the first cohomology class of cocycles for the action of an arbitrary discrete group on an arbitrary measure space and for cocycles with values in an arbitrary compact…

In an earlier paper, we established a natural connection between the Baum-Connes conjecture and noncommutative Bloch theory, viz. the spectral theory of projectively periodic elliptic operators on covering spaces. We elaborate on this…

The Product Conjecture for the homological Bieri-Neumann-Strebel-Renz invariants is proved over a field. Under certain hypotheses the Product Conjecture is shown to also hold over Z, even though D. Schuetz has recently shown that the…

We give an explicit counterexample to an entanglement inequality suggested in a recent paper [quant-ph/0005126] by Benatti and Narnhofer. The inequality would have had far-reaching consequences, including the additivity of the entanglement…

We review the formulation and proof of the Baum-Connes conjecture for the dual of the quantum group $ SU_q(2) $ of Woronowicz. As an illustration of this result we determine the $ K $-groups of quantum automorphism groups of simple matrix…

A vanishing theorem is proved for Ext groups over non-commutative graded algebras. Along the way, an "infinite" version is proved of the non-commutative Auslander-Buchsbaum theorem.

We prove the Strengthened Hanna Neumann Conjecture, in its common graph theoretic formulation. Our original approach to this conjecture used cohomology of sheaves on graphs, although here we give a short combinatorial proof that we found in…

In this short note we give counterexamples to several results related to extension theorems published recently.

The group of piecewise projective homeomorphisms of the line provides straightforward counter-examples to the so-called von Neumann conjecture. The examples are so simple that many additional properties can be established.

In this paper we consider the Baum-Connes correspondence for the affine and extended affine Weyl groups of a compact connected semisimple Lie group. We show that the Baum-Connes correspondence in this context arises from Langlands duality…

Let $X$ be a cohomologically $(n-1)$-complete complex manifold of dimension $n\geq 2$. We prove a vanishing result for the Bott-Chern cohomology group of type $(1, 1)$ with compact support in $X$, which combined with the well-known…