On a conjecture of Atiyah
  In this note we explain how the computation of the spectrum of the lamplighter group from \cite{Grigorchuk-Zuk(2000)} yields a counterexample to a strong version of the Atiyah conjectures about the range of $L^2$-Betti numbers of closed manifolds. 
R.I. Grigorchuk, P. Linnell, T. Schick, and A. Zuk