Property (T) is considered a representation-theoretic form of rigidity, so the Haagerup property may be considered a form of strong nonrigidity; see below for details.
The Haagerup property is interesting to many fields of mathematics, including harmonic analysis, representation theory, operator K-theory, and geometric group theory.
Perhaps its most impressive consequence is that groups with the Haagerup Property satisfy the Baum–Connes conjecture and the related Novikov conjecture.
Groups with the Haagerup property are also uniformly embeddable into a Hilbert space.
be a second countable locally compact group.