Einstein metrics and smooth structures

Details Einstein metrics and smooth structures Einstein metrics and smooth structures

1998-01-16

arxiv.org/abs/math/9801156v1

Geom. Topol. 2 (1998), 1-10

Mathematics

Differential Geometry

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

Scientific paper

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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