-Amalgams IV
-Amalgams V
-Amalgams VI
-Amalgams VII
1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs
We describe unicorn paths in the arc graph and show that they form 1-slim triangles and are invariant under taking subpaths. We deduce that all arc graphs are 7-hyperbolic. Considering the same paths in the arc and curve graph, this also shows that all curve graphs are 17-hyperbolic, including closed surfaces.
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...