 

Claude LeBrun
Scalar curvature, covering spaces, and SeibergWitten theory


Published: 
July 6, 2003

Keywords: 
scalar curvature, Yamabe problem, 4manifold, SeibergWitten invariants 
Subject: 
53C21 (primary); 57R57, 58E11 (secondary) 


Abstract
The Yamabe invariant Y(M)
of a
smooth compact manifold is roughly the supremum of
the scalar curvatures of unitvolume constantscalarcurvature
Riemannian metrics g on M. (To be
precise, one only considers those constantscalarcurvature
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
4manifolds M with Y(M) < 0 have
have finite covering spaces \tilde{M}
with Y(\tilde{M}) > 0.


Acknowledgements
Supported in part by NSF grant DMS0072591.


Author information
Department of Mathematics, Stony Brook University, Stony Brook, NY 11794
claude@math.sunysb.edu
http://www.math.sunysb.edu/~claude/

