Drinfel'd doubles and Ehresmann doubles for Lie algebroids and Lie bialgebroids.
Endomorphisms of the Lie algebroids up to homotopy.
Enveloppe galoisienne d'une application rationnelle de P1.
In 2001, B. Malgrange defines the D-envelope or galoisian envelope of an analytical dynamical system. Roughly speaking, this is the algebraic hull of the dynamical system. In this short article, the D-envelope of a rational map R: P1 --> P1 is computed. The rational maps characterised by a finitness property of their D-envelope appear to be the integrable ones.
Étude des feuilletages transversalement complets et applications
Every orientable 3-manifold is a .
Exponential coordinates and regularity of groupoid heat kernels
We prove that on an asymptotically Euclidean boundary groupoid, the heat kernel of the Laplacian is a smooth groupoid pseudo-differential operator.
Exponential mapping for Lie groupoids
Exponential mapping for Lie groupoids. Applications
Extendibility, monodromy, and local triviality for topological groupoids.
Feuilletages conformes
Dans cet article nous montrons que tout feuilletage conforme, transversalement analytique, de codimension supérieure ou égale à trois sur une variété compacte connexe est transversalement Möbius ou riemannien. Ce théorème peut être vu comme une généralisation, transversalement à un feuilletage, du théorème Ferrand-Obata.
Foliate Partial Holomorphic Structures on Principal Bundles.
Foliated and associated geometric structures on foliated manifolds
Foliation dynamics and leaf invariants.
Formal de Rham theory: irreducible representations of finite simple Lie pseudoalgebras
In this communication, I recall the main results [BDK1] in the classification of finite Lie pseudoalgebras, which generalize several previously known algebraic structures, and announce some new results [BDK2] concerning their representation theory.
Gauge equivalence of Dirac structures and symplectic groupoids
We study gauge transformations of Dirac structures and the relationship between gauge and Morita equivalences of Poisson manifolds. We describe how the symplectic structure of a symplectic groupoid is affected by a gauge transformation of the Poisson structure on its identity section, and prove that gauge-equivalent integrable Poisson structures are Morita equivalent. As an example, we study certain generic sets of Poisson structures on Riemann surfaces: we find complete gauge-equivalence invariants...
Générateurs indépendants pour les systèmes d'isométries de dimension un
Un système fini d’isométries partielles de est dit à générateurs indépendants si les composés non triviaux fixent au plus un point. On décrit un procédé simple et naturel pour obtenir des générateurs indépendants, sans modifier les orbites, pour tout système sans composante minimale homogène : en prenant la restriction de chaque générateur à un certain sous-intervalle de son domaine. Un système avec une composante minimale homogène ne possède pas de générateurs indépendants.
Groupoïde fondamental et d'holonomie de certains feuilletages réguliers
Let M be a manifold with a regular foliation F. We recall the construction of the fundamental groupoid and the homotopy groupoid associated to F. We describe some interesting particular cases and give some glueing techniques. We characterize the cases where these groupoids are Hausdorff spaces.We study in particular both groupoids associated to foliations with Reeb components.
In Ehresmann's footsteps: from group geometries to groupoid geometries
The geometric understanding of Cartan connections led Charles Ehresmann from the Erlangen program of (abstract) transformation groups to the enlarged program of Lie groupoid actions, via the basic concept of structural groupoid acting through the fibres of a (smooth) principal fibre bundle or of its associated bundles, and the basic examples stemming from the manifold of jets (fibred by its source or target projections). We show that the remarkable relation arising between the actions of the structural...
Integrating central extensions of Lie algebras via Lie 2-groups
The purpose of this paper is to show how central extensions of (possibly infinite-dimensional) Lie algebras integrate to central extensions of étale Lie 2-groups in the sense of [Get09, Hen08]. In finite dimensions, central extensions of Lie algebras integrate to central extensions of Lie groups, a fact which is due to the vanishing of for each finite-dimensional Lie group. This fact was used by Cartan (in a slightly other guise) to construct the simply connected Lie group associated to each finite-dimensional...
Isomorphism of intransitive linear Lie equations.