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Monopole classes and Einstein metrics

D. Kotschick
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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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D. Kotschick. 2003-06-01. Monopole classes and Einstein metrics. https://doi.org/10.1155/s1073792804131802

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