Einstein metrics and smooth structures
classification
🧮 math.DG
math.GT
keywords
einsteinsmoothmanifoldsmetricsstructuresthereadmitadmits
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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.
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