Bounded geometry in relatively hyperbolic groups.
Braids: generalizations, presentations and algorithmic properties.
Canonical representatives and equations in hyperbolic groups.
Commensurability of graph products.
Commensurator subgroups of surface groups.
Commutators and squares in free groups.
Compactly supported cohomology of systolic 3-pseudomanifolds
We show that the second group of cohomology with compact supports is nontrivial for three-dimensional systolic pseudomanifolds. It follows that groups acting geometrically on such spaces are not Poincaré duality groups.
Complète réductibilité
La notion de complète réductibilité d’une représentation linéaire peut se définir en termes de l’action de sur l’immeuble de Tits de . Cela suggère une notion analogue pour tous les immeubles sphériques, et donc aussi pour tous les groupes réductifs. On verra comment cette notion se traduit en termes topologiques et quelles applications on peut en tirer.
Computation of five- and six-dimensional Bieberbach groups.
Computational aspects of group extensions and their applications in topology.
Contractibility of deformation spaces of -trees.
Convergence groups from subgroups.
Convex cocompact subgroups of mapping class groups.
Co-rank and Betti number of a group
For a finitely generated group, we study the relations between its rank, the maximal rank of its free quotient, called co-rank (inner rank, cut number), and the maximal rank of its free abelian quotient, called the Betti number. We show that any combination of the group's rank, co-rank, and Betti number within obvious constraints is realized for some finitely presented group (for Betti number equal to rank, the group can be chosen torsion-free). In addition, we show that the Betti number is additive...
Croissance uniforme dans les groupes hyperboliques
On montre qu’un groupe hyperbolique non élémentaire est à croissance uniformément exponentielle, c’est-à-dire qu’il existe une constante strictement plus grande que 1, ne dépendant que du groupe , telle que le taux de croissance exponentiel de relatif à n’importe quel système générateur est plus grand que . On redémontre ce faisant qu’un groupe hyperbolique n’a qu’un nombre fini de classes de conjugaison de sous-groupes finis.
Curvature testing in 3-dimensional metric polyhedral complexes.
Deformation and rigidity of simplicial group actions on trees.
Doubles of groups and hyperbolic LERF 3-manifolds.
Dynamics of out on the boundary of outer space
Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups.