On Higher Eta-Invariants and Metrics of Positive Scalar Curvature

Let N be a closed connected spin manifold admitting one metric ofpositive 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 ₁(N) and dim N, for N to admit an infinite number of metrics of positive scalar curvature that are nonbordant. Mathematics Subject Classifications (2000) 55N22, 19L41.