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Weak amenability of CAT(0) cubical groups
Abstract (from the preprint)
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 pi_z for which the quantities
z^{l(g)} are matrix coefficients. Here l is a length function
on G obtained from the combinatorial distance function on the complex
X.