Related papers: A Baum-Connes conjecture for singular foliations

We prove a reduction of singularities for pairs of foliations by blowing-up, and then investigate the analytic classification of the reduced models. Those reduced pairs of regular foliations are well understood. The case of a regular and a…

In this paper, we verify the $L^p$ coarse Baum-Connes conjecture for spaces with finite asymptotic dimension for $p\in[1,\infty)$. We also show that the $K$-theory of $L^p$ Roe algebras are independent of $p\in(1,\infty)$ for spaces with…

We classify singular foliations admitting a given leaf and a given transverse singular foliation.

We consider contact foliations: objects which generalise to higher dimensions the flow of the Reeb vector field on contact manifolds. We list a number of properties of such foliations, and propose two conjectures about the topological types…

Using the structural theorems developed in [Hua13], we study the deformation theory of coisotropic submanifolds in contact manifolds, under the assumption that the characteristic foliation is nonsingular. In the "middle" dimensions, we find…

In this paper we partly extend the Beauville-Bogomolov decomposition theorem to the singular setting. We show that any complex projective variety of dimension at most five with canonical singularities and numerically trivial canonical class…

In this paper, we connect the rigidity problem and the coarse Baum-Connes conjecture for Roe algebras. In particular, we show that if $X$ and $Y$ are two uniformly locally finite metric spaces such that their Roe algebras are…

We investigate compact Hausdorff foliations on compact Riemannian manifolds in the context of the Gromov-Hausdorff distance theory. We give some sufficient conditions for such foliations to be separated in the Gromov-Hausdorff topology.

We prove that the Farrell-Jones isomorphism conjecture for non-connective algebraic K-theory for a discrete group G and a coefficient ring R holds true if G belongs to the class of groups acting on trees, under certain conditions on G (see…

We express Witten's deformation of Morse functions using deformation to the normal cone and $C^*$-modules. This allows us to obtain asymptotics of the `large eigenvalues'. Our methods extend to Morse functions along a foliation. We…

Let $M$ be a $n$-dimensional complex manifold and $f,g:M\to M$ two distinct holomorphic self-maps. Suppose that $f$ and $g$ coincide on a globally irreducible compact hypersurface $S\subset M$. We show that if one of the two maps is a local…

We prove that Baum-Bott residues vary continuously under smooth deformations of holomorphic foliations. This provides an effective way to compute residues.

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…

We present a list of open questions in the theory of holomorphic foliations, possibly with singularities. Some problems have been around for a while, others are very accessible.

In this work, we study Lie groupoids equipped with multiplicative foliations and the corresponding infinitesimal data. We determine the infinitesimal counterpart of a multiplicative foliation in terms of its core and sides together with a…

Let $G$ and $H$ be finitely generated groups. In this paper, we prove the quantitative coarse Baum--Connes conjecture for the free product $G* H$ under the assumption that the conjecture holds for both $G$ and $H$.

This doctoral thesis has two objectives. The first objective is to introduce a notion of equivalence for singular foliations that preserves their transverse geometry and is compatible with the notions of Morita equivalence of the holonomy…

A singular riemannian foliation on a complete riemannian manifold is said to be riemannian if each geodesic that is perpendicular at one point to a leaf remains perpendicular to every leaf it meets. The singular foliation is said to admit…

Sp\"ath showed that the Alperin-McKay conjecture in the representation theory of finite groups holds if the so-called inductive Alperin-McKay condition holds for all finite simple groups. In a previous article, we showed that the…

We classify nonsingular holomorphic distributions of arbitrary codimension on certain Hopf manifolds. We prove that all holomorphic distribution of codimension k on a generic Hopf manifold is induced by a mononial holomorphic k-form.