Proper actions of wreath products and generalizations

Yves de Cornulier (1, 2) , Yves Stalder (3) , Alain Valette (4)

1 ICJ - Institut Camille Jordan
2 AGL - Algèbre, géométrie, logique
3 LMBP - Laboratoire de Mathématiques Blaise Pascal
4 UNINE - Institut de Mathématiques

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.

Domaines: Théorie des groupes [math.GR]

Yves de Cornulier, Yves Stalder, Alain Valette. Proper actions of wreath products and generalizations. Transactions of the American Mathematical Society, 2012, 364 (6), pp.3159-3184. ⟨10.1090/S0002-9947-2012-05475-4⟩. ⟨hal-00473061⟩