A flat plane that is not the limit of periodic flat planes.
A spelling theorem for staggered generalized 2-complexes, with applications.
Artin Groups and Infinite Coxeter Groups.
Asphericity of symmetric presentations
Using the notion of relative presentation due to Bogley and Pride, we give a new proof of a theorem of Prishchepov on the asphericity of certain symmetric presentations of groups. Then we obtain further results and applications to topology of low-dimensional manifolds.
Cancellation of Abelian groups of finite rank modulo elementary equivalence.
Cogrowth and spectral gap of generic groups
The cogrowth exponent of a group controls the random walk spectrum. We prove that for a generic group (in the density model) this exponent is arbitrarily close to that of a free group. Moreover, this exponent is stable under random quotients of torsion-free hyperbolic groups.
Conformally non-sperical 2-complexes.
Ein verallgemeinerter Gewichtstest mit Anwendungen auf Baumpräsentationen.
Equivalence of geometric and combinatorial Dehn functions.
Estimations de dimensions de Minkowski dans l’espace des groupes marqués
Dans cet article, on montre que l’espace des groupes marqués est un sous-espace fermé d’un ensemble de Cantor dont la dimension de Hausdorff est infinie. On prouve que la dimension de Minkowski de cet espace est infinie en exhibant des sous-ensembles de groupes marqués à petite simplification dont les dimensions de Minkowski sont arbitrairement grandes. On donne une estimation des dimensions de Minkowski de sous-espaces de groupes à un relateur. On démontre enfin que les dimensions de Minkowski...
Groups of finite quasi-projective dimension.
Hyperbolicity of one-relator groups.
groups are almost convex and have a sub-cubic Dehn function.
Le genre d'un groupe nilpotent avec opérateurs.
Nielsen methods in groups with a length function.
Non-amenable finitely presented torsion-by-cyclic groups
Nonpositively curved 2-complexes with isolated flats.
On aspherical presentations of groups.
On exponential growth rates for free groups.
Let Fp be a free group of rank p ≥ 2. It is well-known that, with respect to a p-element generating set, that is, a basis, the exponential growth rate of Fp is 2p-1. We show that the exponential growth rate τ of a group G with respect to a p-element generating set X is 2p-1 if and only if G is free on X; otherwise τ < 2p-1. We also prove that, for any finite generating set X of Fp which is disjoint from X-1, the exponential growth rate τ of Fp with respect to X is 2p-1 if and only if X is...
On infinite Nielsen transformations.