Algèbres de Lie attachées à un feuilletage
Area functionals and Godbillon-Vey cocycles
We investigate the natural domain of definition of the Godbillon-Vey 2- dimensional cohomology class of the group of diffeomorphisms of the circle. We introduce the notion of area functionals on a space of functions on the circle, we give a sufficiently large space of functions with nontrivial area functional and we give a sufficiently large group of Lipschitz homeomorphisms of the circle where the Godbillon-Vey class is defined.
Cohomologie 3-différentiable de l'algèbre de Poisson d'une variété symplectique
On étudie la cohomologie de Chevalley de la représentation adjointe de l’algèbre de Poisson d’une variété symplectique. On obtient en particulier une description explicite de la cohomologie des cochaînes 2 et 3-différentiables.
Differential equations, Spencer cohomology, and computing resolutions.
Existence of star-products on exact symplectic manifolds
It is shown that if a manifold admits an exact symplectic form, then its Poisson Lie algebra has non trivial formal deformations and the manifold admits star-products. The non-formal derivations of the star-products and the deformations of the Poisson Lie algebra of an arbitrary symplectic manifold are studied.
Fibre bundles associated with fields of geometric objects and the structure tensor
Forme canonique sur le dual du fibré transverse
Isomorphism of intransitive linear Lie equations.
Losik cohomology of the Lie algebra of infinitesimal automorphisms of a -structure. II
Losik cohomology of the Lie algebra of infinitesimal automorphisms of a -structure
Non-degenerescence of some spectral sequences
Each Lie algebra of vector fields (e.g. those which are tangent to a foliation) of a smooth manifold définies, in a natural way, a spectral sequence which converges to the de Rham cohomology of in a finite number of steps. We prove e.g. that for all there exists a foliated compact manifold with infinite dimensional.
Note on two compatibility criteria: Jacobi-Mayer bracket vs. differential Gröbner basis.
On the cohomology of vector fields on parallelizable manifolds
In the present paper we determine for each parallelizable smooth compact manifold the second cohomology spaces of the Lie algebra of smooth vector fields on with values in the module . The case of is of particular interest since the gauge algebra of functions on with values in a finite-dimensional simple Lie algebra has the universal central extension with center , generalizing affine Kac-Moody algebras. The second cohomology classifies twists of the semidirect product of with the...
On the first homology of automorphism groups of manifolds with geometric structures
Hermann and Thurston proved that the group of diffeomorphisms with compact support of a smooth manifold M which are isotopic to the identity is a perfect group. We consider the case where M has a geometric structure. In this paper we shall survey on the recent results of the first homology of the diffeomorphism groups which preserve a smooth G-action or a foliated structure on M. We also work in Lipschitz category.
On the real secondary classes of transversely holomorphic foliations
In this paper we study the real secondary classes of transversely holomorphic foliations. We define a homomorphism from the space of the real secondary classes to the space of the complex secondary classes that corresponds to forgetting the transverse holomorphic structure. By using this homomorphism we show, for example, the decomposition of the Godbillon-Vey class into the imaginary part of the Bott class and the first Chern class of the complex normal bundle of the foliation. We show also...
Remarque sur la cohomologie de l'algèbre de Lie des champs de vecteurs sur la sphère
Sur la cohomologie de l'algèbre de Lie des champs de vecteurs de contact formels
Nous démontrons la finitude de la cohomologie de l’algèbre de Lie des champs de vecteurs formels à variables, respectant la forme de contact universelle .
Sur le groupe fondamental d'un feuilletage
Translation of natural operators on manifolds with AHS-structures
We introduce an explicit procedure to generate natural operators on manifolds with almost Hermitian symmetric structures and work out several examples of this procedure in the case of almost Grassmannian structures.