Alain Valette: L^p-compression and equivariant compression for Baumslag-Solitar groups

Let BS(m,n) be a Baumslag-Solitar group. We show that the metric L^p-compression rate of BS(m,n) is 1, while the equivariant L^p-compression rate of BS(m,n) is 1/\min{p,2}, except in the virtually abelian case. The proof goes by embedding BS(m,n) equivariantly and in a bi-Lipschitz way into the product of a tree and a plane with constant nonpositive curvature. This is joint work with Y. Cornulier and D. Dreesen.