161 citations · 918 across the 69 of their papers we have counts for
6 papers · 1 filter
Twist-rigid Coxeter groups
Pierre-Emmanuel Caprace, Piotr Przytycki
We prove that two angle-compatible Coxeter generating sets of a given finitely generated Coxeter group are conjugate provided one of them does not admit any elementary twist. This…
Twin building lattices do not have asymptotic cut-points
Pierre-Emmanuel Caprace, Francois Dahmani, Vincent Guirardel
We show that twin building lattices have linear divergence, which implies that all asymptotic cones are without cut-points.
On the distortion of twin building lattices
Pierre-Emmanuel Caprace, Bertrand Remy
We show that twin building lattices are undistorted in their ambient group; equivalently, the orbit map of the lattice to the product of the associated twin buildings is a quasi-is…
Can an anisotropic reductive group admit a Tits system?
Pierre-Emmanuel Caprace, Timothée Marquis
Seeking for a converse to a well-known theorem by Borel-Tits, we address the question whether the group of rational points G(k) of an anisotropic reductive k-group may admit a spli…
Combinatorial and group-theoretic compactifications of buildings
Pierre-Emmanuel Caprace, Jean Lecureux
Let X be a building of arbitrary type. A compactification of the set Res(X) of spherical residues of X is introduced. We prove that it coincides with the horofunction comp…
Isometry groups of non-positively curved spaces: discrete subgroups
P. -E. Caprace, N. Monod
We study lattices in non-positively curved metric spaces. Borel density is established in that setting as well as a form of Mostow rigidity. A converse to the flat torus theorem is…