La conjecture de Novikov et le groupe de Thompson

Using the index theorem of Connes and Moscovici and the cyclic cocycle associated to a group cocycle, we prove the Novikov conjecture for the generalized Godbillon–Vey cocycle, which has been defined by Tsuboi through area functionals. As a corollary, we get a new proof of the fact that Thompson’s groups T$T$ and F$F$ satisfy the Novikov conjecture.     

Polynome de Hilbert-Samuel dans les algebres enveloppantes et les algebres de groupe

An analogue of the Hilbert-Samuel polynomial is considered with respect to the augmentation ideal of the enveloping algebra of a finite dimensional nilpotent Lie algebra and the group ring of a finitely generated, torsion-free nilpotent group. Then, the Hilbert series of finitely generated modules are rational.      

Analyse de l'espace des phases et calcul pseudo-differential sur le groupe de Heisenberg

We establish pseudo-differential calculus on the Heisenberg group by defining an algebra of operators acting continuously on Sobolev spaces and containing the class of differential operators. Our approach puts into light microlocal directions and completes, with the Littlewood–Paley theory developed by Bahouri et al., a microlocal analysis of the Heisenberg group. To cite this article: H. Bahouri et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Revêtements modérés et groupe fondamenttal de graphe de groupes

Let R be a discrete complete valuation ring, with algebraically closedresidue field. Let X be a semi-stable R-curve, with smooth generic fibre. In this paper we study tame coverings of X.     

Systèmes dynamiques et lois de groupe formel sur les corps finis

Imitating the Lubin's philosophy on nonarchimedean dynamical systems, we prove that every finite family of inversibles series of Fq[[X]] which commute for the law ○ is connected with a finite family of automorphisms of a formal group over Fq. In some cases these formal groups are reduction on Fq of Lubin-Tate formal groups over finite extensions of Qp.     

Sur le noyau sauvage des corps de nombres et le groupe des classes logarithmiques

Résumé.   Nous étudions la -partie du noyau sauvage d'un corps de nombres en liaison avec l'arithmétique des classes logarithmiques, pour les premiers impairs . En particulier nous caractérisons entièrement la propagation de la trivialité du -noyau sauvage dans une -extension de corps totalement réels en termes de ramification logarithmique.

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We study the -part of the wild kernel of a number field for odd prime in connection with the arithmetic of logarithmic -class groups and we characterize the propagation of the triviality of wild kernel in a Galois -extension of totally real fields in terms of logarithmic ramification.

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Received: 5 July 1999; in final form: 10 January 2000 / Published online: 4 May 2001     

Scindements de Heegaard et groupe des homéotopies des petites variétés de Seifert

Sans résuméOblatum 12-XI-1990     

Distance riemannienne,théorème de Rademacher et inégalité de transport sur le groupe des lacets

In this Note, we shall consider the Riemannian distance on loop groups, which will be identified to one introduced by Hino and Ramirez [M. Hino, J.A. Ramirez, Small-time Gaussian behavior of symmetric diffusion semigroups, Ann. Probab. 31 (2003) 1254–1295]. A transportation cost inequality is established. To cite this article: S. Fang, J. Shao, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Connexite et densite des representations irreductibles des groupes de surface dans le groupe general lineaire

We show that any representation of the fundamental group of an orientable surface Σ in GL_n(R) admits a base of neighborhoods in any of which the subset of irreducible representations is a pathwise connected and dense subset, as long as the genus of Σ is big enough.     

Algèbre de Clifford symplectique. Revêtements du groupe symplectique. Indices de Maslov et spineurs symplectiques

Sans résumé

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This article is the developed text of a talk given at the Symposium on Differential Geometry in Debrecen, Hungary, on August 28–September 3, 1975.