Proper actions of lamplighter groups associated with free groups

Abstract

Given a finite group $H$ and a free group $F_n$, we prove that the wreath product $H\wr F_n$ admits a metrically proper, isometric action on a Hilbert space.

6 pages. The part on Hilbert space compression from the first version of this paper, will be incorporated into a more elaborate paper on the subject

Cited by in corpus (1)

• On a class of ${\mathrm{II}}_1$ factors with at most one Cartan subalgebra