-enveloppe d’un difféomorphisme de
-trees and normalization of pseudogroups.
A Fatou-Julia decomposition of transversally holomorphic foliations
A Fatou-Julia decomposition of transversally holomorphic foliations of complex codimension one was given by Ghys, Gomez-Mont and Saludes. In this paper, we propose another decomposition in terms of normal families. Two decompositions have common properties as well as certain differences. It will be shown that the Fatou sets in our sense always contain the Fatou sets in the sense of Ghys, Gomez-Mont and Saludes and the inclusion is strict in some examples. This property is important when discussing...
A generalized global differential calculus : application to invariance under a Lie group. I
A manifold structure for analytic isotropy Lie pseudogroups of infinite type.
A recursion operator for the universal hierarchy equation via Cartan’s method of equivalence
We apply Cartan’s method of equivalence to find a Bäcklund autotransformation for the tangent covering of the universal hierarchy equation. The transformation provides a recursion operator for symmetries of this equation.
Affinoid structures and connections
Algebras of functions on groupoid of some special foliations.
An introduction to loopoids
We discuss a concept of loopoid as a non-associative generalization of Brandt groupoid. We introduce and study also an interesting class of more general objects which we call semiloopoids. A differential version of loopoids is intended as a framework for Lagrangian discrete mechanics.
Calculus on Lie algebroids, Lie groupoids and Poisson manifolds [Book]
Central extensions and reciprocity laws
Charles Ehresmann's concepts in differential geometry
We outline some of the tools C. Ehresmann introduced in Differential Geometry (fiber bundles, connections, jets, groupoids, pseudogroups). We emphasize two aspects of C. Ehresmann's works: use of Cartan notations for the theory of connections and semi-holonomic jets.
Classification of (1,1) tensor fields and bihamiltonian structures
Consider a (1,1) tensor field J, defined on a real or complex m-dimensional manifold M, whose Nijenhuis torsion vanishes. Suppose that for each point p ∈ M there exist functions , defined around p, such that and , j = 1,...,m. Then there exists a dense open set such that we can find coordinates, around each of its points, on which J is written with affine coefficients. This result is obtained by associating to J a bihamiltonian structure on T*M.
Connections, local subgroupoids, and a holonomy Lie groupoid of a line bundle gerbe.
Connections on lie Algebroids and the Weil-Kostant Theorem
Continuous family groupoids.
Déformations 1-différentiables des algèbres de Lie attachées à une variété symplectique ou de contact
Deformations of Lie brackets: cohomological aspects
We introduce a new cohomology for Lie algebroids, and prove that it provides a differential graded Lie algebra which “controls” deformations of the structure bracket of the algebroid.
Dirac structures and dynamical -matrices
The purpose of this paper is to establish a connection between various objects such as dynamical -matrices, Lie bialgebroids, and Lagrangian subalgebras. Our method relies on the theory of Dirac structures and Courant algebroids. In particular, we give a new method of classifying dynamical -matrices of simple Lie algebras , and prove that dynamical -matrices are in one-one correspondence with certain Lagrangian subalgebras of .
Dirac submanifolds and Poisson involutions