Geometry & Topology, Vol. 2 (1998) Paper no. 1, pages 1-10.

Einstein metrics and smooth structures

D Kotschick

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.

AMS subject classification. Primary: 57R55, 57R57, 53C25 Secondary: 14J29

DOI: 10.2140/gt.1998.2.1

E-print: arXiv:math.DG/9801156

Submitted to GT on 8 September 1997. Revised 14 January 1998. Final version accepted on 15 January 1998. Published 16 January 1998.

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D Kotschick
Mathematisches Institut, Universitat Basel, Rheinsprung 21, 4051 Basel, Switzerland
Email: dieter@math-lab.unibas.ch

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