Quelques remarques sur les feuilletages affines
Recognizing sets by means of some of their sections.
Relative cyclic homology and the Bass conjecture.
Résidus des connexions à singularités et classes caractéristiques
Un “théorème des résidus” est donné, qui exprime les classes caractéristiques réelles de dimension d’un fibré principal à l’aide d’une connexion définie seulement au-dessus d’un voisinage du -squelette d’une triangulation de la base. Ce théorème coiffe simultanément la théorie de Chern-Weil, la théorie de l’obstruction modulo torsion, ainsi que des formules du type Riemann-Hurwitz pour les revêtements ramifiés.
Resolutions of moduli spaces and homological stability
We describe partial semi-simplicial resolutions of moduli spaces of surfaces with tangential structure. This allows us to prove a homological stability theorem for these moduli spaces, which often improves the known stability ranges and gives explicit stability ranges in many new cases. In each of these cases the stable homology can be identified using the methods of Galatius, Madsen, Tillmann and Weiss.
Secondary characteristic classes and intermediate Jacobians.
Some partial formulae for Stiefel-Whitney classes of Grassmannians
Stability of the homology of the moduli spaces of Riemann surfaces with spin structure.
Stable Rank 2 Vector Bundles with Chern-Classes c1 = -1, c2 = 4.
Stable splittings associated with Chevalley groups, I.
Stable splittings associated with Chevalley groups, II.
Stiefel-Whitney characteristic classes and parallelizability of Grassmann manifolds
Stiefel-Whitney classes of the flag manifold
Superconnexions, indice local des familles, déterminant de la cohomologie et métriques de Quillen
Sur la suite exacte canonique associée à un fibré principal
Symmetric invariants and cohomology of groups.
The Brown-Peterson homology and nilpotence of the infinite special orthogonal group.
The computation of Stiefel-Whitney classes
The cohomology ring of a finite group, with coefficients in a finite field, can be computed by a machine, as Carlson has showed. Here “compute” means to find a presentation in terms of generators and relations, and involves only the underlying (graded) ring. We propose a method to determine some of the extra structure: namely, Stiefel-Whitney classes and Steenrod operations. The calculations are explicitly carried out for about one hundred groups (the results can be consulted on the Internet).Next,...
The cyclic homology of the group rings.
The Euler Characteristic is the Unique Locally Determined Numerical Homotopy Invariant of Finite Complexes.