In mathematics, the Haagerup property, also known as Gromov's a-T-menability, is a property of groups that is a strong negation of Kazhdan's property (T). 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.
Read more about Haagerup Property: Definitions, Examples
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