A stable cohomotopy refinement of Seiberg-Witten invariants: II

Abstract

The main theorem describes the behaviour of the stable cohomotopy invariant defined in the first article (joint with M. Furuta) in this series of two under the operation of taking connected sums of four-manifolds: The invariant of a connected sum is the smash product (in the sense of equivariant spectra) of the invariants of the respective summands. This provides nonvanishing results even in cases in which both the integer valued Seiberg-Witten invariants and Donaldson invariants have to vanish. As a consequence, one gets new results on diffeomorphism types of decomposable four-manifolds.