Characterizing algebras of -functions on manifolds
Among all -algebras we characterize those which are algebras of -functions on second countable Hausdorff -manifolds.
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 C...des équations de pfaff complètement intégrables à singularité isolée.
Classification of Nash manifolds
A semi-algebraic analytic manifold and a semi-algebraic analytic map are called a Nash manifold and a Nash map respectively. We clarify the category of Nash manifolds and Nash maps.
Classification of principal connections naturally induced on
We consider a vector bundle and the principal bundle of frames of . Let be a principal connection on and let be a linear connection on . We classify all principal connections on naturally given by and .
Closed transverse -forms on compact complex manifolds
Cohomologie basique et dualité des feuilletages riemanniens
Nous démontrons des théorèmes de dualité de Poincaré et de de Rham pour la cohomologie basique et l’homologie des courants transverses invariants d’un feuilletage riemannien.
Cohomologie bornée des surfaces et courants géodésiques
Cohomologie de Bismut-Nualart-Pardoux et cohomologie de Hochschild entière
Cohomologie de dolbeault le long des feuilles de certains feuilletages complexes
La cohomologie de Dolbeault feuilletée mesure l’obstruction à résoudre le problème de Cauchy-Riemann le long des feuilles d’un feuilletage complexe. En utilisant des méthodes de cohomologie des groupes, nous calculons cette cohomologie pour deux classes de feuilletages : i) le feuilletage complexe affine de Reeb de dimension (complexe) 2 sur la variété de Hopf de dimension 5 ; ii) les feuilletages complexes sur le tore hyperbolique (fibration en tores de dimension n au-dessus d’un cercle et de monodromie...
Cohomologie relative de formes non exceptionnelles
Cohomology of the Lagrange complex
Cohomology of the variational complex in the class of exterior forms of finite jet order.
Cohomology Theories In Synthetic Differential Geometry.
Combinatorial differential geometry and ideal Bianchi–Ricci identities II – the torsion case
This paper is a continuation of [2], dealing with a general, not-necessarily torsion-free, connection. It characterizes all possible systems of generators for vector-field valued operators that depend naturally on a set of vector fields and a linear connection, describes the size of the space of such operators and proves the existence of an ‘ideal’ basis consisting of operators with given leading terms which satisfy the (generalized) Bianchi–Ricci identities without corrections.
Combinatorial Hodge Theory and Signature Operator.
Combinatorics of curvature, and the Bianchi identity.
Combinatorics of non-holonomous jets
Comparative smootheology.
Comparing homologies: Cech's theory, singular chains, integral flat chains and integral currents.