A better proof of the Goldman-Parker conjecture.
A finiteness property and an automatic structure for Coxeter groups.
A geometric approach to the almost convexity and growth of some nilpotent groups.
A geometric invariant of discrete groups.
A lower bound to the action dimension of a group.
A non-quasiconvex subgroup of a hyperbolic group with an exotic limit set.
A numerical invariant for finitely generated groups via actions on graphs.
A remark on the intersection of the conjugates of the base of quasi-HNN groups.
A Root System for the Lyons Group.
A spelling theorem for staggered generalized 2-complexes, with applications.
A Stiefel complex for the orthogonal group of a field.
A very short proof of Forester's rigidity result.
Actions de groupes sur les arbres
Actions of discrete groups on nonpositively curved spaces.
Actions of finitely generated groups on -trees
We study actions of finitely generated groups on -trees under some stability hypotheses. We prove that either the group splits over some controlled subgroup (fixing an arc in particular), or the action can be obtained by gluing together actions of simple types: actions on simplicial trees, actions on lines, and actions coming from measured foliations on -orbifolds. This extends results by Sela and Rips-Sela. However, their results are misstated, and we give a counterexample to their statements.The...
Algorithmic verification of quasi-isometry of some HNN-extensions of Abelian groups.
All CAT(0) boundaries of a group of the form H × K are CE equivalent
M. Bestvina has shown that for any given torsion-free CAT(0) group G, all of its boundaries are shape equivalent. He then posed the question of whether they satisfy the stronger condition of being cell-like equivalent. In this article we prove that the answer is "Yes" in the situation where the group in question splits as a direct product with infinite factors. We accomplish this by proving an interesting theorem in shape theory.
Amenability and Ramsey theory
The purpose of this article is to connect the notion of the amenability of a discrete group with a new form of structural Ramsey theory. The Ramsey-theoretic reformulation of amenability constitutes a considerable weakening of the Følner criterion. As a by-product, it will be shown that in any non-amenable group G, there is a subset E of G such that no finitely additive probability measure on G measures all translates of E equally. The analysis of discrete groups will be generalized to the setting...
Amenable group actions on infinite graphs.
Amenable groups and cellular automata
We show that the theorems of Moore and Myhill hold for cellular automata whose universes are Cayley graphs of amenable finitely generated groups. This extends the analogous result of A. Machi and F. Mignosi “Garden of Eden configurations for cellular automata on Cayley graphs of groups” for groups of sub-exponential growth.