La cohomologie basique d'un feuilletage Riemannien est de dimension finie.
La conjecture de Baum-Connes pour un feuilletage sans holonomie de codimension un sur une variété fermée.
In [C2], Baum-Connes state a conjecture for the K-theory of C*-algebras of foliations. This conjecture has been proved by T. Natsume [N2] for C∞-codimension one foliations without holonomy on a closed manifold. We propose here another proof of the conjecture for this class of foliations, more geometric and based on the existence of the Thom isomorphism, proved by A. Connes in [C3]. The advantage of this approach is that the result will be valid for all C0-foliations.
La décomposition dynamique et la différentiabilité des feuilletages des surfaces
Soit un feuilletage singulier d’une surface compacte . Pour analyser la dynamique de , on décompose de façon canonique en sous-surfaces bordées par des courbes transverses à : les composantes de la récurrence de (ensembles quasiminimaux) sont contenues dans les “régions de récurrence” et peuvent être étudiées séparément; par contre dans les autres régions, dites “régions de passage”, la dynamique est triviale. On propose ensuite une définition des feuilletages singuliers de classe sur...
Le graphe d'un feuilletage admettant un système transverse d'équations differentielles.
Le problème d'équivalence pour les pseudogroupes de Lie : méthodes intrinsèques
Leafwise hyperbolicity; a correction.
Leafwise hyperbolicity of proper foliations.
Leaves of foliations with a transverse geometric structure of finite type.
In this short note we find some conditions which ensure that a G foliation of finite type with all leaves compact is a Riemannian foliation of equivalently the space of leaves of such a foliation is a Satake manifold. A particular attention is paid to transversaly affine foliations. We present several conditions which ensure completeness of such foliations.
Leaves of Markov local minimal sets in foliations of codimension one.
The authors continue their study of exceptional local minimal sets with holonomy modeled on symbolic dynamics (called Markov LMS [C-C 1]). Here, an unpublished theorem of G. Duminy, on the topology of semiproper exceptional leaves, is extended to every leaf, semiproper or not, of a Markov LMS. Other topological results on these leaves are also obtained.
Legendrian foliations on almost -manifolds.
Leibniz cohomology for differentiable manifolds
We propose a definition of Leibniz cohomology, , for differentiable manifolds. Then becomes a non-commutative version of Gelfand-Fuks cohomology. The calculations of reduce to those of formal vector fields, and can be identified with certain invariants of foliations.
Lemme de Moser feuilleté et clasifications des variétés de Poisson régulières.
Regular Poisson structures with fixed characteristic foliation F are described by means of foliated symplectic forms. Associated to each of these structures, there is a class in the second group of foliated cohomology H2(F). Using a foliated version of Moser's lemma, we study the isotopy classes of these structures in relation with their cohomology class. Explicit examples, with dim F = 2, are described.
Les feuilles exceptionnelles ne sont pas exceptionnelles.
Les propriétés topologiques des flots riemanniens retrouvées à l'aide du théorème des variétés presque plates.
L'espace des feuilletages d'un espace analytique compact
Nous construisons sur l’ensemble des feuilletages (avec singulariés) d’un espace analytique compact normal une structure analytique complexe. Dans le cas faiblement kählérien, nous montrons qu’à un point frontière de la compactification naturelle de l’espace des feuilletages est encore associé un feuilletage.
Levi-Flat submanifolds and holomorphic extension of foliations
Lie algebras of vector fields and codimension one foliations.
The main result is a Pursell-Shanks type theorem for codimension one foliations. This theorem can be viewed as a partial solution of a hypothetical general version of the theorem of Pursell-Shanks. Several propositions and lemmas on foliations are contained in the proof.
L'invariant de Godbillon-Vey
Local and nice structures of the groupoid of an equivalence relation
Localization of basic characteristic classes
We introduce basic characteristic classes and numbers as new invariants for Riemannian foliations. If the ambient Riemannian manifold is complete, simply connected (or more generally if the foliation is a transversely orientable Killing foliation) and if the space of leaf closures is compact, then the basic characteristic numbers are determined by the infinitesimal dynamical behavior of the foliation at the union of its closed leaves. In fact, they can be computed with an Atiyah-Bott-Berline-Vergne-type...