Weak amenability of CAT(0)-cubical groups

Erik Guentner; Nigel Higson

doi:10.1007/s10711-009-9408-8

Weak amenability of CAT(0)-cubical groups

Erik Guentner, Nigel Higson

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

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 π_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.

Original language	English (US)
Pages (from-to)	137-156
Number of pages	20
Journal	Geometriae Dedicata
Volume	148
Issue number	1
DOIs	https://doi.org/10.1007/s10711-009-9408-8
State	Published - 2010

All Science Journal Classification (ASJC) codes

Geometry and Topology

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title = "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 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.",

author = "Erik Guentner and Nigel Higson",

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AB - 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.

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Weak amenability of CAT(0)-cubical groups

Abstract

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