Localization of group rings and applications to 2-complexes.
Locally finite classical Tits chamber Systems of large order.
Machine calculations in Weyl groups.
Margulis Lemma, entropy and free products
We prove a Margulis’ Lemma à la Besson-Courtois-Gallot, for manifolds whose fundamental group is a nontrivial free product , without 2-torsion. Moreover, if is torsion-free we give a lower bound for the homotopy systole in terms of upper bounds on the diameter and the volume-entropy. We also provide examples and counterexamples showing the optimality of our assumption. Finally we give two applications of this result: a finiteness theorem and a volume estimate for reducible manifolds.
Metric characterizations of spherical and Euclidean buildings.
Morita classes in the homology of automorphism groups of free groups.
Most automorphisms of a hyperbolic group have very simple dynamics
Negatively curved groups and the convergence property. II: Transitivity in negatively curved groups.
Negatively curved groups have the convergence property. I.
New a-T-menable HNN-extensions.
Non-cohérence de certains reseaux non-uniformes dans le groupe des isométries de l’espace hyperbolique
Non-positively curved aspects of Artin groups of finite type.
On a theorem of Baumslag, Dyer and Heller linking group theory and topology
On aspherical presentations of groups.
On centralizers of elements of groups acting on trees with inversions.
On chirality groups and regular coverings of regular oriented hypermaps
We prove that if the Walsh bipartite map of a regular oriented hypermap is also orientably regular then both and have the same chirality group, the covering core of (the smallest regular map covering ) is the Walsh bipartite map of the covering core of and the closure cover of (the greatest regular map covered by ) is the Walsh bipartite map of the closure cover of . We apply these results to the family of toroidal chiral hypermaps induced by the family of toroidal bipartite maps...
On collineation groups of translation planes of order .
On finite subgroups of groups of type VF.
On groups with linear sci growth
We prove that the semistability growth of hyperbolic groups is linear, which implies that hyperbolic groups which are sci (simply connected at infinity) have linear sci growth. Based on the linearity of the end-depth of finitely presented groups we show that the linear sci is preserved under amalgamated products over finitely generated one-ended groups. Eventually one proves that most non-uniform lattices have linear sci.
On irreducible, infinite, nonaffine Coxeter groups
The following results are proved: The center of any finite index subgroup of an irreducible, infinite, nonaffine Coxeter group is trivial; Any finite index subgroup of an irreducible, infinite, nonaffine Coxeter group cannot be expressed as a product of two nontrivial subgroups. These two theorems imply a unique decomposition theorem for a class of Coxeter groups. We also prove that the orbit of each element other than the identity under the conjugation action in an irreducible, infinite, nonaffine...