The total Stiefel-Whitney class of a regular representation

Stiefel-whitney Homology Classes of Quasi-regular Cell Complexes

A quasi-regular cell complex is defined and shown to have a reasonable barycentric subdivision. In this setting, Whitney's theorem that the ^-skeleton of the barycentric subdivision of a triangulated n-manifold is dual to the (n /c)th Stiefel-Whitney cohomology class is proven, and applied to projective spaces, lens spaces and surfaces. 1. QR complexes. A (finite) cell structure on a space X is...

Stiefel - Whitney Currents

A canonically defined mod 2 linear dependency current is associated to each collection v of sections, Vl, . . . , Vm, of a real rank n vector bundle. This current is supported on the linear dependency set of v. It is defined whenever the collection v satisfies a weak measure theoretic condition called "atomicity." Essentially any reasonable collection of sections satisfies this condition, vastl...

The computation of Stiefel-Whitney classes

L’anneau de cohomologie d’un groupe fini, modulo un nombre premier, peut être calculé à l’aide d’un ordinateur, comme l’a montré Carlson. Ici “calculer” signifie trouver une présentation en termes de générateurs et relations, et seul l’anneau (gradué) sous-jacent est en jeu. Nous proposons une méthode pour déterminer certains éléments de structure supplémentaires: classes de Stiefel-Whitney et ...

Stiefel-whitney Classes for Representations of Groups

Associated to a compact Lie group G is the abelian group P(G) of total Stiefel-Whitney classes of representations. In certain cases the rank of P(G) is equal to the number of conjugacy classes of involutions in G. For the symmetric groups Sn, the total Stiefel-Whitney class of the regular representation is highly divisible in P(Sn) and this implies the existence of 'global' Dickson invariants i...

On the Stiefel-whitney Classes of a Manifold. Ii