Weak amenability of CAT(0) cubical groups
Abstract
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 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.
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