Einstein metrics and smooth structures

Abstract

We prove that there are infinitely many pairs of homeomorphic non-diffeomorphic smooth 4-manifolds, such that in each pair one manifold admits an Einstein metric and the other does not. We also show that there are closed 4-manifolds with two smooth structures which admit Einstein metrics with opposite signs of the scalar curvature.

10 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol2/paper1.abs.html

References in corpus (1)

• A simply connected numerical Godeaux surface with ample canonical class

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