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 cohomology algebras of orientable Seifert manifolds and applications to Lusternik-Schnirelmann category
This note gives a complete description of the cohomology algebra of any orientable Seifert manifold with ℤ/p coefficients, for an arbitrary prime p. As an application, the existence of a degree one map from an orientable Seifert manifold onto a lens space is completely determined. A second application shows that the Lusternik-Schnirelmann category for a large class of Seifert manifolds is equal to 3, which in turn is used to verify the Ganea conjecture for these Seifert manifolds.
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 cyclic homology of the group rings.
The -term of the descent spectral sequence for continuous -spectra.
The envelope of a subcategory in topology and group theory.
The Euler class and periodicity of group cohomology.
The exact sequence in the homology of groups with integral coefficients modulo associated to two normal subgroups
The geometric invariants of direct products of virtually free groups.
The geometry of abstract groups and their splittings.
A survey of splitting theorems for abstract groups and their applications. Topics covered include preliminaries, early results, Bass-Serre theory, the structure of G-trees, Serre's applications to SL2 and length functions. Stallings' theorem, results about accessibility and bounds for splittability. Duality groups and pairs; results of Eckmann and collaborators on PD2 groups. Relative ends, the JSJ theorems and the splitting results of Kropholler and Roller on PDn groups. Notions of quasi-isometry,...
The Gray filtration on phantom maps
This paper is a study of the Gray index of phantom maps. We give a new, tower theoretic, definition of the Gray index, which allows us to study the naturality properties of the Gray index in some detail. McGibbon and Roitberg have shown that if f* is surjective on rational cohomology, then the induced map on phantom sets is also surjective. We show that if f* is surjective just in dimension k, then f induces a surjection on a certain subquotient of the phantom set. If the condition...
The Homological Algebra of Artin Groups.
The Homological Dimension of an Abelian Group as a Module over its Ring of Endomorphisms. III.
The Homological Dimension of an Abelian Group as a Module over Its Ring of Endomorphisms. II.
The homology of Peiffer products of groups.
The integral homology of SL2 and PSL2 of euclidean imaginary quadratic integers.
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.