On the topology of scalar-flat manifolds

Anand Dessai

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On the topology of scalar-flat manifolds

Anand Dessai

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Abstract

Let $M$ be a simply-connected closed manifold of dimension $\geq 5$ 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 $\geq 5$ 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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Anand Dessai. 2000-06-21. On the topology of scalar-flat manifolds. https://arxiv.org/abs/math/0006149

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