Foldable cubical complexes of nonpositive curvature.
Folner sets of alternate directed groups
An explicit family of Folner sets is constructed for some directed groups acting on a rooted tree of sublogarithmic valency by alternate permutations. In the case of bounded valency, these groups were known to be amenable by probabilistic methods. The present construction provides a new and independent proof of amenability, using neither random walks, nor word length.
For Coxeter groups is a coefficient of a uniformly bounded representation
We prove the theorem in the title by constructing an action of a Coxeter group on a product of trees.