Abstract
For a given smooth four-manifold we study the relation between the simple type condition for Donaldson invariants and the intersections of basic classes with smoothly embedded spheres with self-intersection −2 and −3. Studying the structure of Donaldson invariants imposed by the existence of embedded spheres we also recover one criterion for a manifold being of simple type (previously proven by Kronheimer and Mrówka using singular connections).
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