Curvature, Covering Spaces, and Seiberg-Witten Theory

Claude LeBrun

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arXiv · math/0110329

Curvature, Covering Spaces, and Seiberg-Witten Theory

Claude LeBrun

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Abstract

The Yamabe invariant Y(M) of a smooth compact manifold is roughly the supremum of the scalar curvatures of unit-volume constant-scalar-curvature Riemannian metrics g on M. (To be precise, one only considers those constant-scalar-curvature metrics which are Yamabe minimizers, but this technicality does not, e.g. affect the sign of the answer.) In this article, it is shown that many 4-manifolds M with Y(M) < 0 have have finite covering spaces \tilde{M} with Y(\tilde{M}) > 0.

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BibTeX RIS

Claude LeBrun. 2003-07-11. Curvature, Covering Spaces, and Seiberg-Witten Theory. https://arxiv.org/abs/math/0110329

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