Geometriae Dedicata

, Volume 124, Issue 1, pp 199–211 | Cite as

Wreath products with the integers, proper actions and Hilbert space compression



We prove that the properties of acting metrically properly on some space with walls or some CAT(0) cube complex are closed by taking the wreath product with \({\mathbb{Z}}\) . We also give a lower bound for the (equivariant) Hilbert space compression of \({H\wr\mathbb{Z}}\) in terms of the (equivariant) Hilbert space compression of H.


Wreath products Proper (group) actions Compression Hilbert spaces Trees CAT(0) cube complexes 

Mathematics Subject Classifications

Primary: 20E22 Secondary: 20E08 20F69 


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© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Laboratoire de MathématiquesUniversité Blaise PascalAubière CedexFrance
  2. 2.Institut de MathématiquesUniversité de NeuchâtelNeuchâtelSwitzerland

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