arXiv math/03060222003-06-01math.DGmath.GT

Monopole classes and Einstein metrics

D. Kotschick

备注：: 17 pages. Includes an Appendix on ``Ricci-flat four-manifolds'' by D. Kotschick and J. Wehrheim
发表信息：: Int. Math. Res. Not. 2004:12 (2004), 593--609.
DOI：: 10.1155/S1073792804131802

英文摘要：

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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