Stable cohomotopy Seiberg-Witten invariants of connected sums of four-manifolds with positive first Betti number II: Applications

This is a sequel to our article [16] where a generalization of a nonvanishing theorem for stable cohomotopy Seiberg-Witten invariants is proved. The main purpose of the current article is to give various applications of the non-vanishing theorem to the differential geometry and topology of 4-manifolds, including existence of exotic smooth structures, smooth connected sum decompositions of 4-manifolds and computations of Perelman's lambda. invariant.