Weak amenability of CAT(0) cubical groups

Details Weak amenability of CAT(0) cubical groups Weak amenability of CAT(0) cubical groups

2007-02-20

arxiv.org/abs/math/0702568v1

Mathematics

Operator Algebras

22 pages

Scientific paper

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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