Groups with the Haagerup Property : Gromovs a-T-menability

A locally compact group has the Haagerup property, or is a-T-menable in the sense of Gromov, if it admits a proper isometric action on some affine Hilbert space. As Gromovs pun is trying to indicate, this definition is designed as a strong negation to Kazhdans property (T), characterized by the fact that every isometric action on some affine Hilbert space has a fixed point. This book is to covers various aspects of the Haagerup property. It gives several new examples.