Parallelism in diagram geometry.
Point-line characterizations of Lie geometries.
Polyèdres finis de dimension 2 à courbure et de rang 2
On définit localement la notion de polyèdre de rang deux pour un polyèdre fini de dimension deux à courbure négative ou nulle. On montre que le revêtement universel d’un tel espace est soit le produit de deux arbres, soit un immeuble de Tits euclidien de rang deux.
Polyhedra with specified links
Property (T) and groups
We show that each group in a class of finitely generated groups introduced in [2] and [3] has Kazhdan’s property (T), and calculate the exact Kazhdan constant of with respect to its natural set of generators. These are the first infinite groups shown to have property (T) without making essential use of the theory of representations of linear groups, and the first infinite groups with property (T) for which the exact Kazhdan constant has been calculated. These groups therefore provide answers...
Random walk on a building of type Ãr and brownian motion of the Weyl chamber
In this paper we study a random walk on an affine building of type Ãr, whose radial part, when suitably normalized, converges toward the brownian motion of the Weyl chamber. This gives a new discrete approximation of this process, alternative to the one of Biane (Probab. Theory Related Fields89 (1991) 117–129). This extends also the link at the probabilistic level between riemannian symmetric spaces of the noncompact type and their discrete counterpart, which had been previously discovered by Bougerol...
Rank three geometries associated with .
Receding polar regions of a spherical building and the center conjecture
We introduce the notion of a polar region of a spherical building and use some simple observations about polar regions to give elementary proofs of various fundamental properties of root groups. We combine some of these observations with results of Timmesfeld, Balser and Lytchak to give a new proof of the center conjecture for convex chamber subcomplexes of thick spherical buildings.
Réseaux de Coxeter-Davis et commensurateurs
For each integer and each finite graph , we construct a Coxeter group and a non positively curved polygonal complex on which acts properly cocompactly, such that each polygon of has edges, and the link of each vertex of is isomorphic to . If is a “generalized -gon”, then is a Tits building modelled on a reflection group of the hyperbolic plane. We give a condition on for to be non enumerable (which is satisfied if is a thick classical generalized -gon). On the other hand,...
Some Amalgams of type 2A6 in a field of characteristic 3
Sur les polyèdres de rang 2
The generating rank of the symplectic line-Grassmannian.
The rank 2 geometries of the simple Suzuki groups .
The residually weakly primitive geometries of .
The tree of life and other affine buildings.
The uniqueness of groups of type J4.
Three amalgams of A_5
Using the Frattini subgroup and independent generating sets to study RWPri geometries.
Причесывание треугольных билдингов