Stable cohomotopy Seiberg-Witten invariants of connected sums of four-manifolds with positive first Betti number, I: Non-vanishing theorem

摘要

We shall prove a new non-vanishing theorem for the stable cohomotopy Seiberg-Witten invariant [S. Bauer and M. Furuta, Stable cohomotopy refinement of Seiberg-Witten invariants: I, Invent. Math. 155 (2004) 1-19; S. Bauer, Stable cohomotopy refinement of Seiberg-Witten invariants: II, Invent. Math. 155 (2004) 21-40.] of connected sums of 4-manifolds with positive first Betti number.