Title
Planar lamplighter group is not of negative type
Abstract
We prove that the 1/2-snowflake of the lamplighter group over the planar integer grid does not admit a biLipschitz embedding into Hilbert space (this property is called not having a negative type). In particular it does not admit a bi-Lipschitz embedding into L_1. We will discuss basics in metric embeddings, geometric group theory and the role of Poincaré-type inequalities as obstructions for metric embeddability. This is joint work with G. Antonelli, N. Cavallucci, L. Nalon, A. Naor and P. Wald.
