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

15 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

Access to Document

10.1007/s10711-009-9408-8

Cite this

@article{d2fb106cb9f7464391736c4179b094cd,

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",

note = "Funding Information: The authors were partially supported by grants from the US National Science Foundation.",

year = "2010",

doi = "10.1007/s10711-009-9408-8",

language = "English (US)",

volume = "148",

pages = "137--156",

journal = "Geometriae Dedicata",

issn = "0046-5755",

publisher = "Springer Netherlands",

number = "1",

}

TY - JOUR

T1 - Weak amenability of CAT(0)-cubical groups

AU - Guentner, Erik

AU - Higson, Nigel

N1 - Funding Information: The authors were partially supported by grants from the US National Science Foundation.

PY - 2010

Y1 - 2010

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=77957111565&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957111565&partnerID=8YFLogxK

U2 - 10.1007/s10711-009-9408-8

DO - 10.1007/s10711-009-9408-8

M3 - Article

AN - SCOPUS:77957111565

SN - 0046-5755

VL - 148

SP - 137

EP - 156

JO - Geometriae Dedicata

JF - Geometriae Dedicata

IS - 1

ER -

Weak amenability of CAT(0)-cubical groups

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this