The Auslander-Reiten Quiver of a Finite Group.
The Chern classes modulo of a regular representation. (Les classes de Chern modulo d'une représentation régulière.)
The complex of words and Nakaoka stability.
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 Euler class and periodicity of group cohomology.
The Johnson homomorphism and the second cohomology of .
The Kazhdan property of the mapping class group of closed surfaces and the first cohomology group of its cofinite subgroups.
The lower central series of a fiber-type arrangement.
The normalizer splitting conjecture for p-compact groups
Let X be a p-compact group, with maximal torus BT → BX, maximal torus normalizer BN and Weyl group . We prove that for an odd prime p, the fibration has a section, which is unique up to vertical homotopy.
The Obstruction theory of Group Extensions and H^3(Q, A) in Abstract Categories
Thick subcategories of the stable module category
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...
Torsors and special extensions
Travaux de Quillen sur la cohomologie des groupes