2001/10/31 by Claude LeBrun
Mathematics · #math.DG #math.GT #msc:53C27 #msc:57R57
published as New York Journal of Mathematics 9 (2003) 93-97, see http://nyjm.albany.edu:8000/j/2003/9-7.html · Source file for published version. Discussion expanded, minor errors corrected. 8 pages, LaTeX2e
arxiv created 2003/07/11 · arxiv updated 2009/11/30
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 M with Y(M) > 0.