The question is in the title:
Do one-relator groups satisfy Haagerup property?
I think the answer is known at least in some specific cases, but is the problem completely solved?
The question is in the title:
Do one-relator groups satisfy Haagerup property?
I think the answer is known at least in some specific cases, but is the problem completely solved?
As far as I know, the problem is not solved, but much is known. The canonical reference is the suggestively named Groups with Haagerup property: Gromov's a-T-menability, by Cherix, Cowling, Jolissant, Julig, Valette. See, in particular, Theorem 6.3.1 and Chapter 7