Finiteness properties of soluble arithmetic groups over global function fields.
Finitude géométrique en géométrie de Hilbert
On étudie la notion de finitude géométrique pour certaines géométries de Hilbert définies par un ouvert strictement convexe à bord de classe .La définition dans le cadre des espaces Gromov-hyperboliques fait intervenir l’action du groupe discret considéré sur le bord de l’espace. On montre, en construisant explicitement un contre-exemple, que cette définition doit être renforcée pour obtenir des définitions équivalentes en termes de la géométrie de l’orbifold quotient, similaires à celles obtenues...
Flats in 3-manifolds
Flats in Spaces with Convex Geodesic Bicombings
In spaces of nonpositive curvature the existence of isometrically embedded flat (hyper)planes is often granted by apparently weaker conditions on large scales.We show that some such results remain valid for metric spaces with non-unique geodesic segments under suitable convexity assumptions on the distance function along distinguished geodesics. The discussion includes, among other things, the Flat Torus Theorem and Gromov’s hyperbolicity criterion referring to embedded planes. This generalizes...
Flows and joins of metric spaces.
Foldable cubical complexes of nonpositive curvature.
Følner sequences in polycyclic groups.
The isoperimetric inequality |∂Ω| / |Ω| = constant / log |Ω| for finite subsets Ω in a finitely generated group Γ with exponential growth is optimal if Γ is polycyclic.
Folner sets of alternate directed groups
An explicit family of Folner sets is constructed for some directed groups acting on a rooted tree of sublogarithmic valency by alternate permutations. In the case of bounded valency, these groups were known to be amenable by probabilistic methods. The present construction provides a new and independent proof of amenability, using neither random walks, nor word length.
For Coxeter groups is a coefficient of a uniformly bounded representation
We prove the theorem in the title by constructing an action of a Coxeter group on a product of trees.
Formal language theory and the geometry of 3-manifolds.