94 citations · 159 across the 15 of their papers we have counts for
15 papers · 1 filter
Quasi-isometric invariance of continuous group -cohomology, and first applications to vanishings
Marc Bourdon, Bertrand Remy
We show that the continuous -cohomology of locally compact second countable groups is a quasi-isometric invariant. As an application, we prove partial results supporting a pos…
Wonderful compactifications of Bruhat-Tits buildings
Bertrand Remy, Amaury Thuillier, Annette Werner
Given a split semisimple group over a local field, we consider the maximal Satake-Berkovich compactification of the corresponding Euclidean building. We prove that it can be equiva…
On some pro-p groups from infinite-dimensional Lie theory
Inna Capdeboscq, Bertrand Remy
We initiate the study of some pro-p-groups arising from infinite-dimensional Lie theory. These groups are completions of some subgroups of incomplete Kac-Moody groups over finite f…
Simplicity of twin tree lattices with non-trivial commutation relations
Pierre-Emmanuel Caprace, Bertrand Remy
We prove a simplicity criterion for certain twin tree lattices. It applies to all rank two Kac-Moody groups over finite fields with non-trivial commutation relations, thereby yield…
Bruhat-Tits buildings and analytic geometry
Bertrand Remy, Amaury Thuillier, Annette Werner
This paper provides an overview of the theory of Bruhat-Tits buildings. Besides, we explain how Bruhat-Tits buildings can be realized inside Berkovich spaces. In this way, Berkovic…
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…
Bruhat-Tits theory from Berkovich's point of view. II. Satake compactifications
Bertrand Remy, Amaury Thuillier, Annette Werner
In our previous paper "Bruhat-Tits theory from Berkovich's point of view. I ? Realizations and compactifications of buildings", we investigated realizations of the Bruhat-Tits buil…
Contraction groups in complete Kac-Moody groups
Udo Baumgartner, Jacqui Ramagge, Bertrand Remy
Let be an abstract Kac-Moody group over a finite field and be the closure of the image of in the automorphism group of its positive building. We show that if the…
Simplicity and superrigidity of twin building lattices
Pierre-Emmanuel Caprace, Bertrand Remy
Kac-Moody groups over finite fields are finitely generated groups. Most of them can naturally be viewed as irreducible lattices in products of two closed automorphism groups of non…
Flat rank of automorphism groups of buildings
Udo Baumgartner, Bertrand Remy, George A. Willis
The flat rank of a totally disconnected locally compact group G, denoted flat-rk(G), is an invariant of the topological group structure of G. It is defined thanks to a natural dist…
Kac-Moody groups as discrete groups
Bertrand Remy
This survey paper presents the discrete group viewpoint on Kac-Moody groups. Over finite fields, the latter groups are finitely generated; they act on new buildings enjoying remark…
Commensurators of some non-uniform tree lattices and Moufang twin trees
Peter Abramenko, Bertrand Remy
Sh. Mozes showed that the commensurator of the lattice is dense in the full automorphism group of the Bruhat-Tits tree of valency $p+…
Topological simplicity, commensurator super-rigidity and non-linearities of Kac-Moody groups
Bertrand Remy, Patrick Bonvin
We provide new arguments to see topological Kac-Moody groups as generalized semisimple groups over local fields: they are products of topologically simple groups and their Iwahori…
Kac-Moody groups: split and relative theories. Lattices
Bertrand Remy
In this survey article, we recall some facts about split Kac-Moody groups as defined by J. Tits, describe their main properties and then propose an analogue of Borel-Tits theory fo…
Topological groups of Kac-Moody type, Fuchsian twinnings and their lattices
Bertrand Remy, Mark Ronan
This paper deals with a class of totally disconnected groups acting on buildings, among which are certain Kac-Moody groups. The apartments of our buildings are hyperbolic planes ti…