On higher eta-invariants and metrics of positive scalar curvature

Let N be a closed connected spin manifold admitting one metric of positive scalar curvature. In this paper we use the higher eta-invariant associated to the Dirac operator on N in order to distinguish metrics of positive scalar curvature on N. In particular, we give sufficient conditions, involving pi(1)(N) and dim N, for N to admit an infinite number of metrics of positive scalar curvature that are nonbordant.