Curvature, Covering Spaces, and Seiberg-Witten Theory

Details Curvature, Covering Spaces, and Seiberg-Witten Theory Curvature, Covering Spaces, and Seiberg-Witten Theory

2001-10-31

arxiv.org/abs/math/0110329v2

New York Journal of Mathematics 9 (2003) 93-97, see http://nyjm.albany.edu:8000/j/2003/9-7.html

Mathematics

Differential Geometry

Source file for published version. Discussion expanded, minor errors corrected. 8 pages, LaTeX2e

Scientific paper

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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