Projective bundles.
Projective planes of order 10 do not have a collineation of order 3.
Projective planes of order 12 do not have a non-abelian group of order 6 as a collineation group.
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...
Pseudodual grids and extensions of generalized quadrangles.
Pseudo-ovals, elation Laguerre planes, and translation generalized quadrangles.
Quadratische Identitäten bei Polygonen.
Quasifibrations.
Quasifields with irreducible nuclei.
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 .
Rank three residually connected geometries for , revisited.
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.
Recherches analytiques sur la surface du troisième ordre qui est la réciproque de la surface de Steiner
Recursive constructions for skew resolutions in affine geometries.
Reflection loops of spaces with congruence and hyperbolic incidence structure
In an absolute space with congruence there are line reflections and point reflections. With the help of point reflections one can define in a natural way an addition + of points which is only associative if the product of three point reflection is a point reflection again. In general, for example for the case that is a linear space with hyperbolic incidence structure, the addition is not associative. is a K-loop or a Bruck loop.
Regular conditional linear spaces with two consecutive line degrees.
Regular hyperbolic fibrations.
Regular linear spaces.
Regular partial conical flocks.