Related papers: A Baum-Connes conjecture for singular foliations

We introduce a new method for studying the Baum-Connes conjecture, which we call the direct splitting method. The method can simplify and clarify proofs of some of the known cases of the conjecture. In a separate paper, with J. Brodzki, E.…

We present a geometric approach to the Baum-Connes conjecture with coefficients for Gromov monster groups via a theorem of Khoskham and Skandalis. Secondly, we use recent results concerning the a-T-menability at infinity of large girth…

First, we shall formulate and prove Theorem of Lie-Kolchin type for a cone and derive some algebro-geometric consequences. Next, inspired by a recent result of Dinh and Sibony we pose a conjecture of Tits type for a group of automorphisms…

We prove the Baum-Connes conjecture for hyperbolic groups and their subgroups.

Recent discoveries make it possible to compute the K-theory of certain rings from their cyclic homology and certain versions of their cdh-cohomology. We extend the work of G. Corti\~nas et al. who calculated the K-theory of, in addition to…

In a previous paper ([1]), we associated a holonomy groupoid and a C*-algebra to any singular foliation (M,F). Using these, we construct the associated pseudodifferential calculus. This calculus gives meaning to a Laplace operator of any…

We give a new proof of some cases of the Baum-Connes conjecture along the lines of a proof of the Farrell-Jones conjecture.

We study general properties of exotic crossed-product functors and characterise those which extend to functors on equivariant C*-algebra categories based on correspondences. We show that every such functor allows the construction of a…

We extend the concept of orbifold to that of branchfold, in order to allow any cone singularities with rational angles, and show why branchfolds naturally fit in the theory of branched coverings. Then, we obtain a geometric goodness theorem…

This article studies codimension one foliations on projective man-ifolds having a compact leaf (free of singularities). It explores the interplay between Ueda theory (order of flatness of the normal bundle) and the holo-nomy representation…

Replaces Previous version. Includes comments on poincare duality for twisted equivariant in the context of proper and discrete actions and the Baum-Connes Conjecture. We use a spectral sequence proposed by C. Dwyer and previous work by…

Given an ample groupoid, we construct a spectral sequence with groupoid homology with integer coefficients on the second sheet, converging to the K-groups of the (reduced) groupoid C*-algebra, provided the groupoid has torsion-free…

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.

We give a superconnection proof of Connes' index theorem for proper cocompact actions of etale groupoids. This includes Connes' general foliation index theorem for foliations with Hausdorff holonomy groupoid.

We give a new construction of the holonomy and fundamental groupoids of a singular foliation. In contrast with the existing construction of Androulidakis and Skandalis, our method proceeds by taking a quotient of an infinite dimensional…

Using methods from coarse topology we show that fundamental classes of closed enlargeable manifolds map non-trivially both to the rational homology of their fundamental groups and to the K-theory of the corresponding reduced C*-algebras.…

In this paper we study the Lie groupoids which appear in foliation theory. A foliation groupoid is a Lie groupoid which integrates a foliation, or, equivalently, whose anchor map is injective. The first theorem shows that, for a Lie…

Transversally K\"ahler foliations are a generalisation of K\"ahler manifolds, appearing naturally in the complex non-K\"ahler setting. We give a self-contained proof of how the classical methods used in the proof of the Aubin-Yau theorem…

In this article we study the cohomological and homological (due to Jannsen) Hodge conjecture for singular varieties. The motivation for studying singular varieties comes from the fact that any smooth projective variety X is birational to a…

These lecture notes attempt to invite the reader towards the theory of singular foliations, both smooth and holomorphic. In addition to a systematic review of the foundations, and an attempt to put in order examples and several elementary…