On Higher Eta-Invariants and Metrics of Positive Scalar Curvature

Leichtnam, Eric
Piazza, Paolo

¹Research partially supported by a CNR-CNRS cooperation project.
²Institut de Jussieu-Chevaleret, Plateau E, 7^me étage (Algébres d'opérateurs), 175 rue de Chevaleret, 75013 Paris, France. e-mail: [email protected]

^*Research partially supported by a CNR-CNRS cooperation project and by MURST.

^**Università di Roma ‘La Sapienza’, Dipartimento di Matematica ‘Guido Castelnuovo’, P.le A. Moro 2, I-00185 Roma, Italy. e-mail: [email protected]

K-Theory 24(4):p 341-359, December 2001.

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 π₁(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.