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Sur l’homologie des groupes orthogonaux et symplectiques à coefficients tordus

Aurélien Djament, Christine Vespa (2010)

Annales scientifiques de l'École Normale Supérieure

On calcule dans cet article l’homologie stable des groupes orthogonaux et symplectiques sur un corps fini k à coefficients tordus par un endofoncteur usuel F des k -espaces vectoriels (puissance extérieure, symétrique, divisée...). Par homologie stable, on entend, pour tout entier naturel i , les colimites des espaces vectoriels H i ( O n , n ( k ) ; F ( k 2 n ) ) et H i ( Sp 2 n ( k ) ; F ( k 2 n ) ) — dans cette situation, la stabilisation (avec une borne explicite en fonction de i et F ) est un résultat classique de Charney. Tout d’abord, nous donnons un cadre...

The computation of Stiefel-Whitney classes

Pierre Guillot (2010)

Annales de l’institut Fourier

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 normalizer splitting conjecture for p-compact groups

Kasper Andersen (1999)

Fundamenta Mathematicae

Let X be a p-compact group, with maximal torus BT → BX, maximal torus normalizer BN and Weyl group W X . We prove that for an odd prime p, the fibration B T → B N → B W X has a section, which is unique up to vertical homotopy.

Thick subcategories of the stable module category

D. Benson, Jon Carlson, Jeremy Rickard (1997)

Fundamenta Mathematicae

We study the thick subcategories of the stable category of finitely generated modules for the principal block of the group algebra of a finite group G over a field of characteristic p. In case G is a p-group we obtain a complete classification of the thick subcategories. The same classification works whenever the nucleus of the cohomology variety is zero. In case the nucleus is nonzero, we describe some examples which lead us to believe that there are always infinitely many thick subcategories concentrated...

Currently displaying 101 – 120 of 125