Product preserving bundles on foliated manifolds
We present a complete description of all product preserving bundle functors on the category ℱol of all foliated manifolds and their leaf respecting maps in terms of homomorphisms of Weil algebras.
Profondeur homotopique et conjecture de grothendieck
Projective Connections in CR Geometry.
Projective limits of Banach vector bundles.
Projective varieties invariant by one-dimensional foliations.
Projective varieties with non-residually finite fundamental group
Projectively Anosov flows with differentiable (un)stable foliations
We consider projectively Anosov flows with differentiable stable and unstable foliations. We characterize the flows on which can be extended on a neighbourhood of into a projectively Anosov flow so that is a compact leaf of the stable foliation. Furthermore, to realize this extension on an arbitrary closed 3-manifold, the topology of this manifold plays an essential role. Thus, we give the classification of projectively Anosov flows on . In this case, the only flows on which extend to ...
Prolongement des champs de vecteurs à des variétés de points proches
Prolongement des homotopies, -variétés et cycles tangents
Nous montrons que le prolongement des homotopies, propriété de certains feuilletages étudiée par Godbillon, équivaut à la réunion de trois conditions indépendantes : la condition de Barre, qui est transverse ; la trivialité des cycles évanouissants de toutes dimensions, et la trivialité des cycles apparents de toutes dimensions. On établit que pour les feuilletages riemanniens et pour les feuilletages géodésibles, la propriété équivaut à l’absence d’holonomie. Ces résultats sont ensuite appliqués...
Properties of Pseudo-holomorphic Curves in Symplectisations II: Embedding Controls and Algebraic Invariants.
Properties of pseudoholomorphic curves in symplectisations. I : asymptotics
Pseudo-differential operators on V-manifolds and foliations (II).
This paper is a continuation of Part I of the same title which has appeared at the last issue of this journal.
Pseudo-isotopies de plongements en codimension 2
Publier sous l’occupation I. Autour du cas de Jacques Feldbau et de l’Académie des sciences
C’est un article sur les publications mathématiques pendant l’Occupation (1940–44). À travers les cas de quatre mathématiciens, et surtout de celui de Jacques Feldbau (un des fondateurs de la théorie des fibrés, mort en déportation), nous étudions la façon dont la censure a frappé les mathématiciens français définis comme juifs par le « Statut des juifs » d’octobre 1940 et les stratégies de publication que ceux-ci ont alors utilisées (pseudonymes, plis cachetés, journaux provinciaux...) La manière...
Quadratische Formen und Monodromiegruppen von Singularitäten.
Quantum classifying spaces and universal quantum characteristic classes
A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced and analyzed. Interrelations with the abstract algebraic theory of quantum characteristic classes are discussed. Various non-equivalent approaches to defining universal characteristic classes are outlined.
Quantum invariants of periodic links and periodic 3-manifolds
We give criteria for framed links and 3-manifolds to be periodic of prime order. As applications we show that the Poincaré sphere is of periodicity 2, 3, 5 only and the Brieskorn sphere Σ(2,3,7) is of periodicity 2, 3, 7 only.
Quantum mechanics and nonabelian theta functions for the gauge group SU(2)
We propose a direction of study of nonabelian theta functions by establishing an analogy between the Weyl quantization of a one-dimensional particle and the metaplectic representation on the one hand, and the quantization of the moduli space of flat connections on a surface and the representation of the mapping class group on the space of nonabelian theta functions on the other. We exemplify this with the cases of classical theta functions and of the nonabelian theta functions for the gauge group...
Quantum principal bundles and their characteristic classes
A general theory of characteristic classes of quantum principal bundles is presented, incorporating basic ideas of classical Weil theory into the conceptual framework of noncommutative differential geometry. A purely cohomological interpretation of the Weil homomorphism is given, together with a geometrical interpretation via quantum invariant polynomials. A natural spectral sequence is described. Some interesting quantum phenomena appearing in the formalism are discussed.
Quantum faithfully detects mapping class groups modulo center.