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Infinitely presented small cancellation groups have the Haagerup property
We prove the Haagerup property (= Gromov's a-T-menability) for finitely generated groups defined by infinite presentations satisfying the C'(1/6)-small cancellation condition. We deduce that these groups are coarsely embeddable into a Hilbert space and that the strong Baum–Connes conjecture holds for them. The result is a first nontrivial advancement in …