Minimal genus for 4-manifolds with b+ = 1

Abstract

We derive an adjunction inequality for any smooth, closed, connected, oriented 4-manifold X with b+ = 1. This inequality depends only on the cohomology algebra and generalizes the inequality of Strle in the case of b1 = 0. We demonstrate that the inequality is especially powerful when 2~χ + 3σ ≥ 0, where ~χ is the modified Euler number taking account of the cup product on H1(X;).