We prove that if G is a discrete group that admits a metrically proper action on a finite-dimensional CAT(0) cube complex X, then G is weakly amenable. We do this by constructing uniformly bounded Hilbert space representations πz for which the quantities zℓ(g) are matrix coefficients. Here ℓ is a length function on G obtained from the combinatorial distance function on the complex X.
All Science Journal Classification (ASJC) codes
- Geometry and Topology