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Proper actions of wreath products and generalizations

Abstract : We study stability properties of the Haagerup property and of coarse embeddability in a Hilbert space, under certain semidirect products. In particular, we prove that they are stable under taking standard wreath products. Our construction also allows for a characterization of subsets with relative Property T in a standard wreath product.
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Yves de Cornulier, Yves Stalder, Alain Valette. Proper actions of wreath products and generalizations. Transactions of the American Mathematical Society, American Mathematical Society, 2012, 364 (6), pp.3159-3184. ⟨10.1090/S0002-9947-2012-05475-4⟩. ⟨hal-00473061⟩

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