-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.
À propos des deuxième et troisième espaces de cohomologie de l'algèbre de Lie de Poisson d'une variété symplectique
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
Algebraic characterizations of the algebra of functions and of the Lie algebra of vector fields of a manifold
Algebras of functions on groupoid of some special foliations.
Algèbres de Lie attachées à un feuilletage
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.
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.
Calculus on Lie algebroids, Lie groupoids and Poisson manifolds [Book]
Cancellative semigroups on manifolds.
Central extensions and reciprocity laws
Characteristic Homomorphisms of Regular Lie Algebroids
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.