Monopole classes and Einstein metrics

2003/06/01 by D. Kotschick
Mathematics · #math.DG #math.GT #msc:57R57 #msc:53C25 #msc:57R55

paper · pdf · doi:10.1155/s1073792804131802

published as Int. Math. Res. Not. 2004:12 (2004), 593--609. · 17 pages. Includes an Appendix on ``Ricci-flat four-manifolds'' by D. Kotschick and J. Wehrheim

arxiv created 2003/06/01 · arxiv updated 2009/11/30

Abstract

We introduce the notion of a special monopole class on a four-manifold. This is used to prove restrictions on the smooth structures of Einstein manifolds. As an application we prove that there are Einstein four-manifolds which are simply connected, spin, and satisfy the strict Hitchin--Thorpe inequality, and which are homeomorphic to manifolds without Einstein metrics. In the Appendix, written with J. Wehrheim, we use special monopole classes to discuss the classification of Ricci-flat four-manifolds.

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