Quasi-bigèbres jacobiennes
Remarque sur la cohomologie de l'algèbre de Lie des champs de vecteurs sur la sphère
Remarques sur les systèmes différentiels
Representations of étale Lie groupoids and modules over Hopf algebroids
The classical Serre-Swan's theorem defines an equivalence between the category of vector bundles and the category of finitely generated projective modules over the algebra of continuous functions on some compact Hausdorff topological space. We extend these results to obtain a correspondence between the category of representations of an étale Lie groupoid and the category of modules over its Hopf algebroid that are of finite type and of constant rank. Both of these constructions are functorially...
Rigidity of homogeneous contact manifolds under Fano deformation.
Separatrices for non solvable dynamics on
We define the separatrices for pseudogroups of diffeomorphisms of open neighbourhoods of the origin in the complex plane and prove their existence for non solvable pseudogroups (Theorem 1). This extends a result by Shcherbakov (in [21]) accurately. Our method also applies to prove the topological rigidity theorem for generic pseudogroups attributed to Shcherbakov (dans [20]).
Some Remarks on Dirac Structures and Poisson Reductions
Dirac structures are characterized in terms of their characteristic pairs defined in this note and then Poisson reductions are discussed from the point of view of Dirac structures.
Some remarks on the cohomology of the Poisson algebra
Structure of symmetry groups via Cartan's method: survey of four approaches.
Sur certains pseudogroupes de biholomorphismes locaux de
On montre que si est un pseudogroupe de transformations locales holomorphes de en zéro contenant deux éléments “en position générale” et proches de l’identité, alors : 1) L’action de sur le fibré des jets d’ordre infini sur un petit voisinage épointé de est minimale (c’est-à-dire que si et si est un germe de biholomorphisme alors il existe une suite qui converge vers uniformément au voisinage de ). 2) ne préserve aucune structure géométrique au voisinage de (c’est une conséquence...
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
Tangent lifts of higher order of multiplicative Dirac structures
The tangent lifts of higher order of Dirac structures and some properties have been defined in [9] and studied in [11]. By the same way, the tangent lifts of higher order of Poisson structures have been studied in [10] and some applications are given. In particular, the authors have studied the nature of the Lie algebroids and singular foliations induced by these lifting. In this paper, we study the tangent lifts of higher order of multiplicative Poisson structures, multiplicative Dirac structures...
Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU (N) groups.
The deformation theory of representations of fundamental groups of compact Kähler manifolds
The Euler-Poincaré-Hopf theorem for flat connections in some transitive Lie algebroids
This paper is a continuation of [19], [21], [22]. We study flat connections with isolated singularities in some transitive Lie algebroids for which either or or are isotropy Lie algebras. Under the assumption that the dimension of the isotropy Lie algebra is equal to , where is the dimension of the base manifold, we assign to any such isolated singularity a real number called an index. For -Lie algebroids, this index cannot be an integer. We prove the index theorem (the Euler-Poincaré-Hopf...
The modular class of a Poisson map
We introduce the modular class of a Poisson map. We look at several examples and we use the modular classes of Poisson maps to study the behavior of the modular class of a Poisson manifold under different kinds of reduction. We also discuss their symplectic groupoid version, which lives in groupoid cohomology.
The monodromy groupoid of a Lie groupoid
The Weil algebra and the Van Est isomorphism
This paper belongs to a series of papers devoted to the study of the cohomology of classifying spaces. Generalizing the Weil algebra of a Lie algebra and Kalkman’s BRST model, here we introduce the Weil algebra associated to any Lie algebroid . We then show that this Weil algebra is related to the Bott-Shulman complex (computing the cohomology of the classifying space) via a Van Est map and we prove a Van Est isomorphism theorem. As application, we generalize and find a simpler more conceptual...
Théorie des déformations de structures