Monopole classes and Einstein metrics
微分几何
2007-05-23 v1 几何拓扑
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.
引用
@article{arxiv.math/0306022,
title = {Monopole classes and Einstein metrics},
author = {D. Kotschick},
journal= {arXiv preprint arXiv:math/0306022},
year = {2007}
}
备注
17 pages. Includes an Appendix on ``Ricci-flat four-manifolds'' by D. Kotschick and J. Wehrheim