New York Journal of Mathematics
Volume 9 (2003) 93-97


Claude LeBrun

Scalar curvature, covering spaces, and Seiberg-Witten theory

Published: July 6, 2003
Keywords: scalar curvature, Yamabe problem, 4-manifold, Seiberg-Witten invariants
Subject: 53C21 (primary); 57R57, 58E11 (secondary)

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.


Supported in part by NSF grant DMS-0072591.

Author information

Department of Mathematics, Stony Brook University, Stony Brook, NY 11794