Connected-sum vanishing of the Seiberg–Witten invariant
= Connected-sum vanishing of the Seiberg–Witten invariant
If a closed oriented <smooth four-manifold> splits as a <connected sum> $X_1\#X_2$ with both $b_2^+(X_i)>0$, its ordinary <Seiberg–Witten invariants of a four-manifold> vanish. Combined with <Taubes nonvanishing theorem>, this obstructs a symplectic structure in that orientation.