Donaldson invariants of 4-manifolds with simple type
Let \(X\) be a simply-connected 4-manifold of simple type. The authors give a proof of Kronheimer-Mrowka's structure theorem for the Donaldson series of \(X\) which avoids the use of singular connections. Furthermore they prove a result analogous to Kronheimer-Mrowka's lower bound for the genus of embedded surfaces of non-negative self-intersection: the smooth surface is replaced by an immersed sphere, possibly of negative self-intersection. In fact two results are the key ingredients in the proof of the structure theorem: the blow-up formula for simple type 4-manifolds (previously proved by Kronheimer-Mrowka and the authors), and results on the effect on the Donaldson series of embedded spheres of negative self-intersection which are proved in this paper.
scientific article; zbMATH DE number 892615