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ON THE TOPOLOGY OF SCALAR-FLAT MANIFOLDS
Published online by Cambridge University Press: 09 April 2001
Abstract
Let M be a simply connected closed manifold of dimension greater than 4 which does not admit a metric with positive scalar curvature. We give necessary conditions for M to admit a scalar-flat metric. These conditions involve the first Pontrjagin class and the cohomology ring of M. As a consequence, any simply connected scalar-flat manifold of dimension greater than 4 with vanishing first Pontrjagin class admits a metric with positive scalar curvature. We also describe some relations between scalar-flat metrics, almost complex structures and the free loop space.
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- © The London Mathematical Society 2001