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Hilbert space compression and exactness of discrete groups

Hilbert space compression and exactness of discrete groups
Hilbert space compression and exactness of discrete groups
We show that the Hilbert space compression of any (unbounded) finite-dimensional CAT(0) cube complex is 1 and deduce that any finitely generated group acting properly, co-compactly on a CAT(0) cube complex is exact, and hence has Yu's Property A. The class of groups covered by this theorem includes free groups, finitely generated Coxeter groups, finitely generated right angled Artin groups, finitely presented groups satisfying the B(4)–T(4) small cancellation condition and all those word-hyperbolic groups satisfying the B(6) condition. Another family of examples is provided by certain canonical surgeries defined by link diagrams.
exactness, Hilbert space compression, CAT(0) cube complex, property A
0022-1236
292-305
Campbell, Sarah
e6d6f15a-72d1-4397-9ff4-c89fae2cd440
Niblo, Graham A.
43fe9561-c483-4cdf-bee5-0de388b78944
Campbell, Sarah
e6d6f15a-72d1-4397-9ff4-c89fae2cd440
Niblo, Graham A.
43fe9561-c483-4cdf-bee5-0de388b78944

Campbell, Sarah and Niblo, Graham A. (2005) Hilbert space compression and exactness of discrete groups. Journal of Functional Analysis, 222 (2), 292-305. (doi:10.1016/j.jfa.2005.01.012).

Record type: Article

Abstract

We show that the Hilbert space compression of any (unbounded) finite-dimensional CAT(0) cube complex is 1 and deduce that any finitely generated group acting properly, co-compactly on a CAT(0) cube complex is exact, and hence has Yu's Property A. The class of groups covered by this theorem includes free groups, finitely generated Coxeter groups, finitely generated right angled Artin groups, finitely presented groups satisfying the B(4)–T(4) small cancellation condition and all those word-hyperbolic groups satisfying the B(6) condition. Another family of examples is provided by certain canonical surgeries defined by link diagrams.

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Published date: 2005
Keywords: exactness, Hilbert space compression, CAT(0) cube complex, property A

Identifiers

Local EPrints ID: 29821
URI: https://eprints.soton.ac.uk/id/eprint/29821
ISSN: 0022-1236
PURE UUID: 4604dbfa-2250-424d-a071-ca5dfc2bd4b6

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Date deposited: 11 May 2006
Last modified: 17 Jul 2017 15:56

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