On the Homology Theory of Central Group Extensions II. The Exact Sequence in the General Case
On the Schur Multipliers of Steinberg and Chevalley Groups over Commutative Rings.
Partially defined cocycles and the Maslov index for a local ring
In this paper we study some aspects of the cohomology of groups and we construct a central extension of the symplectic group .
Perturbations of centre-fixing dynamical systems.
p-Nilpotence, classifying space indecomposability, and other properties of almost all finite groups.
Poincaré Duality and Groups of Type (FP).
Polynomial Maps on Groups. II.
Presentations of finite simple groups: a computational approach
All finite simple groups of Lie type of rank over a field of size , with the possible exception of the Ree groups , have presentations with at most 49 relations and bit-length . Moreover, and have presentations with 3 generators; 7 relations and bit-length , while has a presentation with 6 generators, 25 relations and bit-length .
Realizing maps between modules over Tate cohomology rings.
Resolutions of moduli spaces and homological stability
We describe partial semi-simplicial resolutions of moduli spaces of surfaces with tangential structure. This allows us to prove a homological stability theorem for these moduli spaces, which often improves the known stability ranges and gives explicit stability ranges in many new cases. In each of these cases the stable homology can be identified using the methods of Galatius, Madsen, Tillmann and Weiss.
Salvetti complex, spectral sequences and cohomology of Artin groups
The aim of this short survey is to give a quick introduction to the Salvetti complex as a tool for the study of the cohomology of Artin groups. In particular we show how a spectral sequence induced by a filtration on the complex provides a very natural and useful method to study recursively the cohomology of Artin groups, simplifying many computations. In the last section some examples of applications are presented.
Séries de compositions de modules instables et injectivité de la cohomologie du groupe Z/2.
Some algebraic applications of graded categorical group theory.
Spectral sequences and relative cohomology
Stable cohomology of alternating groups
We determine the stable cohomology groups ( of the alternating groups for all integers n and i, and all odd primes p.
Stable rational cohomology of automorphism groups of free groups and the integral cohomology of moduli spaces of graphs.
It is not known whether or not the stable rational cohomology groups H*(Aut(F∞);Q) always vanish (see Hatcher in [5] and Hatcher and Vogtmann in [7] where they pose the question and show that it does vanish in the first 6 dimensions). We show that either the rational cohomology does not vanish in certain dimensions, or the integral cohomology of a moduli space of pointed graphs does not stabilize in certain other dimensions. Similar results are stated for groups of outer automorphisms. This yields...
Sur la cohomologie des formes quadratiques
Sur le module des relations d'un p-groupe et la suite exacte d'inflation-restriction.
Sur le multiplicateur de Schur d’un -groupe
Sur les groupes de tresses