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Pierre Guillot
The computation of Stiefel-Whitney classes
(Le calcul des classes de Stiefel-Whitney)
Annales de l'institut Fourier, 60 no. 2 (2010), p. 565-606, doi: 10.5802/aif.2533
Article PDF | Reviews MR 2667787 | Zbl pre05726205
Class. Math.: 20J06, 57R20, 65K05, 14C15
Keywords: Cohomology of groups, characteristic classes, algorithms, computers, chow rings

Résumé - Abstract

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, we give an application: thanks to the new information gathered, we can in many cases determine which cohomology classes are supported by algebraic varieties.

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