Volume 2, issue 1 (1998)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Einstein metrics and smooth structures

Dieter Kotschick

Geometry & Topology 2 (1998) 1–10

arXiv: math.DG/9801156

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.

Keywords
Einstein metric, smooth structure, 4–manifold
Mathematical Subject Classification
Primary: 57R55, 57R57, 53C25
Secondary: 14J29
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Publication
Received: 8 September 1997
Revised: 14 January 1998
Accepted: 15 January 1998
Published: 16 January 1998
Proposed: Peter Kronheimer
Seconded: Ronald Stern, Gang Tian
Authors
Dieter Kotschick
Mathematisches Institut
Universität Basel
Rheinsprung 21
4051 Basel
Switzerland