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21.30 (2026)

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(Well-known question). A discrete group $G$ is said to have the Haagerup property (also known as Gromov’s a-T-menability property) if there exists a metrically proper isometric action of $G$ on a (possibly infinite-dimensional) Hilbert space. Are all 1-relator groups Haagerup groups?

Contributor: J. O. Button

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