Abstract. Let $M$ be an even dimensional manifold with $\pi_1(M)=\Bbb Z_\ell$ for $\ell=2^\nu\ge2$. We assume that the universal cover $\tilde M$ is $spin$. We shall define $N(M)=\tilde M \times \tilde M/\Bbb Z_{2\ell}$ and establishe a relation between the eta invariant of $M$ and the eta invariant of $N(M)$. We use this to study the moduli space of metrics of positive scalar curvature on the manifold $M$.
AMSclassification. Primary 55N15; Secondary 58G12
Keywords. Moduli space, eta invariant