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Property A and CAT(0) cube complexes

Property A and CAT(0) cube complexes
Property A and CAT(0) cube complexes
Property A is a non-equivariant analogue of amenability defined for metric spaces. Euclidean spaces and trees are examples of spaces with Property A. Simultaneously generalising these facts, we show that finite-dimensional CAT(0) cube complexes have Property A. We do not assume that the complex is locally finite. We also prove that given a discrete group acting properly on a finite-dimensional CAT(0) cube complex the stabilisers of vertices at infinity are amenable.
geometric group theory, analysis, amenability, Yu's property A, CAT(0) cube complex
0022-1236
1408-1431
Brodzki, J.
b1fe25fd-5451-4fd0-b24b-c59b75710543
Campbell, S.J.
e6d6f15a-72d1-4397-9ff4-c89fae2cd440
Guentner, E.
d5edf540-5285-45f6-93cc-5809c0fcd285
Niblo, G.A.
43fe9561-c483-4cdf-bee5-0de388b78944
Wright, N.J.
f4685b8d-7496-47dc-95f0-aba3f70fbccd
Brodzki, J.
b1fe25fd-5451-4fd0-b24b-c59b75710543
Campbell, S.J.
e6d6f15a-72d1-4397-9ff4-c89fae2cd440
Guentner, E.
d5edf540-5285-45f6-93cc-5809c0fcd285
Niblo, G.A.
43fe9561-c483-4cdf-bee5-0de388b78944
Wright, N.J.
f4685b8d-7496-47dc-95f0-aba3f70fbccd

Brodzki, J., Campbell, S.J., Guentner, E., Niblo, G.A. and Wright, N.J. (2009) Property A and CAT(0) cube complexes. Journal of Functional Analysis, 256 (5), 1408-1431. (doi:10.1016/j.jfa.2008.10.018).

Record type: Article

Abstract

Property A is a non-equivariant analogue of amenability defined for metric spaces. Euclidean spaces and trees are examples of spaces with Property A. Simultaneously generalising these facts, we show that finite-dimensional CAT(0) cube complexes have Property A. We do not assume that the complex is locally finite. We also prove that given a discrete group acting properly on a finite-dimensional CAT(0) cube complex the stabilisers of vertices at infinity are amenable.

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More information

Published date: 1 March 2009
Keywords: geometric group theory, analysis, amenability, Yu's property A, CAT(0) cube complex
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 69508
URI: https://eprints.soton.ac.uk/id/eprint/69508
ISSN: 0022-1236
PURE UUID: 46b545e7-2503-4462-9cbd-af0f296d2238
ORCID for G.A. Niblo: ORCID iD orcid.org/0000-0003-0648-7027
ORCID for N.J. Wright: ORCID iD orcid.org/0000-0003-4884-2576

Catalogue record

Date deposited: 10 Nov 2009
Last modified: 29 Aug 2019 00:53

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