Monopole classes and Einstein metrics
Abstract
Description
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.
17 pages. Includes an Appendix on ``Ricci-flat four-manifolds'' by D. Kotschick and J. Wehrheim
17 pages. Includes an Appendix on ``Ricci-flat four-manifolds'' by D. Kotschick and J. Wehrheim