Limit groups and groups acting freely on -trees.
Limit groups for relatively hyperbolic groups. II: Makanin-Razborov diagrams.
Limits of (certain) CAT(0) groups. I: Compactification.
Moufang trees and generalized quadrangles.
Moyennabilité intérieure et extensions HNN
On présente des conditions suffisantes pour qu’une extension HNN soit intérieurement moyennable, respectivement CCI, qui donnent des critères nécessaires et suffisants parmi les groupes de Baumslag-Solitar. On en déduit qu’un tel groupe, vu comme groupe d’automorphismes de son arbre de Bass-Serre, possède des éléments non triviaux qui fixent des sous-arbres non bornés.
On asymptotic dimension of groups.
On centralizers of elements of groups acting on trees with inversions.
On commuting elemts of groups acting on trees
On computing quaternion quotient graphs for function fields
Let be a maximal -order in a division quaternion algebra over which is split at the place . The present article gives an algorithm to compute a fundamental domain for the action of the group of units on the Bruhat-Tits tree associated to . This action is a function field analog of the action of a co-compact Fuchsian group on the upper half plane. The algorithm also yields an explicit presentation of the group in terms of generators and relations. Moreover we determine an upper bound...
On invertor elements and finitely generated subgroups of groups acting on trees with inversions.
On Parabolic Subgroups and Hecke Algebras of some Fractal Groups
* The authors thank the “Swiss National Science Foundation” for its support.We study the subgroup structure, Hecke algebras, quasi-regular representations, and asymptotic properties of some fractal groups of branch type. We introduce parabolic subgroups, show that they are weakly maximal, and that the corresponding quasi-regular representations are irreducible. These (infinite-dimensional) representations are approximated by finite-dimensional quasi-regular representations. The Hecke algebras...
On the intersection of finitely generated subgroups of free groups.
Products of trees, lattices and simple groups.
R-trees and the Bieri-Neumann-Strebel invariant.
Let G be a finitely generated group. We give a new characterization of its Bieri-Neumann-Strebel invariant Σ(G), in terms of geometric abelian actions on R-trees. We provide a proof of Brown's characterization of Σ(G) by exceptional abelian actions of G, using geometric methods.
Self-similar Lie algebras
We give a general definition of branched, self-similar Lie algebras, and show that important examples of Lie algebras fall into that class. We give sufficient conditions for a self-similar Lie algebra to be nil, and prove in this manner that the self-similar algebras associated with Grigorchuk’s and Gupta–Sidki’s torsion groups are nil as well as self-similar.We derive the same results for a class of examples constructed by Petrogradsky, Shestakov and Zelmanov.
Simplicial approximation and low-rank trees.
Simplicity of Neretin's group of spheromorphisms
Denote by , , the regular tree whose vertices have valence , its boundary. Yu. A. Neretin has proposed a group of transformations of , thought of as a combinatorial analogue of the diffeomorphism group of the circle. We show that is generated by two groups: the group of tree automorphisms, and a Higman-Thompson group . We prove the simplicity of and of a family of its subgroups.
Small cancellation theory and automatic groups.
Small cancellation theory and automatic groups: Part II.
Spectral deformations of automorphic functions over graphs of groups.