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Characterization of the Haagerup property by fibred coarse embedding into Hilbert space
Author(s) -
Chen Xiaoman,
Wang Qin,
Wang Xianjin
Publication year - 2013
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdt045
Subject(s) - fibered knot , mathematics , embedding , pure mathematics , hilbert space , finitely generated abelian group , space (punctuation) , group (periodic table) , property (philosophy) , linguistics , philosophy , epistemology , artificial intelligence , computer science , chemistry , organic chemistry
We show that a finitely generated, residually finite group has the Haagerup property (Gromov's a‐T‐menability) if and only if one (or equivalently, all) of its box spaces admits a fibred coarse embedding into Hilbert space. In contrast, the box spaces of a finitely generated, residually finite hyperbolic group with property (T) do not admit a fibred coarse embedding into Hilbert space, but do admit a fibred coarse embedding into an ℓ p ‐space for some p >2.