The computation of Stiefel-Whitney classes
نویسنده
چکیده
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 opérations de Steenrod. Les calculs sont concrètement menés pour une centaine de groupes (les résultats sont consultables en détails sur Internet). Nous donnons ensuite une application: à l’aide des nouvelles informations obtenues, nous pouvons dans de nombreux cas déterminer quelles sont les classes de cohomologie qui sont supportées par des cycles algébriques.
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