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Weak amenability of CAT(0) cubical groups

Nigel Higson·Erik Guentner
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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 z^{l(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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Nigel Higson, Erik Guentner. 2007-02-20. Weak amenability of CAT(0) cubical groups. https://arxiv.org/abs/math/0702568

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