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

Abstract : 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 \Z . We also give a lower bound for the (equivariant) Hilbert space compression of H\wr\Z in terms of the (equivariant) Hilbert space compression of H.
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Yves Stalder, Alain Valette. Wreath products with the integers, proper actions and Hilbert space compression. Geometriae Dedicata, Springer Verlag, 2007, 124, pp.199-211. ⟨10.1007/s10711-006-9119-3⟩. ⟨hal-00472504⟩

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