Related papers: On the Baum-Connes conjecture for $D_{\infty}$

We prove an analogue of the Baum-Connes conjecture for free orthogonal quantum groups. More precisely, we show that these quantum groups have a $ \gamma $-element and that $ \gamma = 1 $. It follows that free orthogonal quantum groups are $…

We prove a generalized version of the Strong Atiyah Conjecture for the infinite dihedral group W, replacing the group von Neumann algebra NW with the Hecke-von Neumann algebra N_qW.

Bourbaki seminar 1062, October 2012.

We review the Burghelea conjecture, which constitutes a full computation of the periodic cyclic homology of complex group rings, and its relation to the algebraic Baum-Connes conjecture. The Burghelea conjecture implies the Bass conjecture.…

In this paper, we use the KK-theory of Kasparov to prove exactness of sequences relating the K-theory of a real C^*-algebra and of its complexification (generalizing results of Boersema). We use this to relate the real version of the…

The main purpose of this paper is to modify the orbit method for the Baum-Connes conjecture as developed by Chabert, Echterhoff and Nest in their proof of the Connes-Kasparov conjecture for almost connected groups \cite{MR2010742} in order…

We give a survey of the meaning, status and applications of the Baum-Connes Conjecture about the topological K-theory of the reduced group C^*-algebra and the Farrell-Jones Conjecture about the algebraic K- and L-theory of the group ring of…

Let $\left( 1\to N_m\to G_m\to Q_m\to 1 \right)_{m\in \mathbb{N}}$ be a sequence of extensions of finite groups such that their coarse disjoint unions have bounded geometry. In this paper, we show that if the coarse disjoint unions of…

We study the possibility of applying a finite-dimensionality argument in order to address parts of the Baum-Connes conjecture for finitely generated linear groups. This gives an alternative approach to the results of Guentner, Higson, and…

We study a Going-Down (or restriction) principle for ample groupoids and its applications. The Going-Down principle for locally compact groups was developed by Chabert, Echterhoff and Oyono-Oyono and allows to study certain functors, that…

We describe the infinite dihedral group as automaton group. We collect basic results and give full proofs in details for all statements.

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…

We give a decomposition of the equivariant Kasparov category for discrete quantum group with torsions. As an outcome, we show that the crossed product by a discrete quantum group in a certain class preserves the UCT. We then show that…

We give a new criterion for solvability of group equations, providing proofs of various generalizations of the Kervaire-Laudenbach conjecture for Connes-embeddable groups.

We show that the Baum-Connes morphism twisted by a non-unitary representation, defined in [GA08], is an isomorphism for a large class of groups satisfying the Baum-Connes conjecture. Such class contains all the real semi-simple Lie groups,…

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…

The relative Novikov conjecture states that the relative higher signatures of manifolds with boundary are invariant under orientation-preserving homotopy equivalences of pairs. In this paper, we study the relative Baum-Connes assembly map…

Given a (not necessarily discrete) proper metric space $M$ with bounded geometry, we define a groupoid $G(M)$. We show that the coarse Baum--Connes conjecture with coefficients, which states that the assembly map with coefficients for G(M)…

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, we investigate the $L^{p}$ coarse Baum-Connes conjecture for $p\in [1,\infty)$ via $C_{0}$ coarse structure, which is a refinement of the bounded coarse structure on a metric space. We prove that the $C_{0}$ version of the…