Related papers: The Baum-Connes conjecture with coefficients for w…
We prove the Baum-Connes conjecture for hyperbolic groups and their subgroups.
This paper gives a proof of the Baum-Connes conjecture with coefficients for hyperbolic groups. More precisely the injectivity of the Baum-Connes map was established by Kasparov and Skandalis and we prove the surjectivity.
We construct a strongly bolic metric for a certain class of relatively hyperbolic groups, which includes those with CAT(0) parabolics and virtually abelian parabolics. If we further assume that the parabolics satisfy (RD), applying a…
We study a group which is hyperbolic relative to a finite family of infinite subgroups. We show that the group satisfies the coarse Baum-Connes conjecture if each subgroup belonging to the family satisfies the coarse Baum-Connes conjecture…
We prove the Borel Conjecture for a class of groups containing word-hyperbolic groups and groups acting properly, isometrically and cocompactly on a finite dimensional CAT(0)-space.
By deploying dense subalgebras of $\ell^1(G)$ we generalize the Bass conjecture in terms of Connes' cyclic homology theory. In particular, we propose a stronger version of the $\ell^1$-Bass Conjecture. We prove that hyperbolic groups…
This note provides a counterexample showing that the assumptions that Chabert and Echterhoff have imposed in their permanence property of the Baum-Connes conjecture for group extensions cannot be simplified.
In this paper, we introduce a notion of stable coarse algebras for metric spaces with bounded geometry, and formulate the twisted coarse Baum--Connes conjecture with respect to stable coarse algebras. We prove permanence properties of this…
We prove that many Artin groups of large type satisfy the rapid decay property, including all those of extra-large type. For many of these, including all 3-generator groups of extra-large type, a result of Lafforgue applies to show that the…
We give a new proof of some cases of the Baum-Connes conjecture along the lines of a proof of the Farrell-Jones conjecture.
This is the text of my Bourbaki seminar on the proof of the surface subgroup conjecture by Jeremy Kahn and Vladimir Markovic.
We prove the Baum--Connes conjecture with arbitrary coefficients for some classes of groups: (1) Linear algebraic groups over a non-archimedean local field. (2) Linear algebraic groups over the adeles of a global field k, provided that at…
We make an exposition of the proof of the Baum-Connes conjecture for the infinite dihedral group following the ideas of Higson and Kasparov.
For a fixed word hyperbolic group we compare different residual properties related to quasiconvex subgroups.
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…
In this note, we exhibit a method to prove the Baum-Connes conjecture (with coefficients) for extensions with finite quotients of certain groups which already satisfy the Baum-Connes conjecture. Interesting examples to which this method…
We prove the K-theoretic Farrell-Jones Conjecture for hyperbolic groups with (twisted) coefficients in any associative ring with unit.
This is a Bourbaki's seminar text. We introduce the combinatorial Kashiwara-Vergne conjecture on the Baker-Campbell-Hausdorff serie. After recalling previous results and consequences, we explain the Alekseev-Meinrenken's proof…
These notes grew out of a mini-course given from May 13th to May 17th at UQAM in Montreal during a workshop on Diophantine Approximation and Value Distribution Theory. We start with an overview of Lang-Vojta's conjectures on…
We survey the known results regarding the boundaries of word-hyperbolic groups.