Geometriae Dedicata

, Volume 124, Issue 1, pp 199–211

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


DOI: 10.1007/s10711-006-9119-3

Cite this article as:
Stalder, Y. & Valette, A. Geom Dedicata (2007) 124: 199. doi:10.1007/s10711-006-9119-3


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 productsProper (group) actionsCompressionHilbert spacesTreesCAT(0) cube complexes

Mathematics Subject Classifications

Primary: 20E22Secondary: 20E0820F69

Copyright information

© 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