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… (More)

Let Γ be an arithmetic lattice in an absolutely simple Lie group G with trivial centre. We prove that there exists an integer N ≥ 2, a subgroup Λ of finite index in Γ, and an action of Λ on Z such… (More)

The geodesic distance between points in real hyperbolic space is a hypermetric, and hence is a kernel negative type. The proof given here uses an integral formula for geodesic distance, in terms of a… (More)

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our… (More)

We study growth of 1-cocycles of locally compact groups, with values in unitary representations. Discussing the existence of 1-cocycles with linear growth, we obtain the following alternative for a… (More)

Let Γ be a group, and let CΓ be the group ring of Γ over C . We first give a simplified and self-contained proof of Zalesskii’s theorem [23] that the canonical trace on CΓ takes rational values on… (More)

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… (More)

We exploit the isomorphism between the first p-cohomology H1 (p)(Γ) and the reduced 1-cohomology with coefficients in p(Γ), to obtain vanishing results for H1 (p)(Γ): we treat e.g. groups acting on… (More)