Some refined higher type adjunction inequalities on 4-manifolds

Abstract

We further sharpen higher type adjunction inequalities of P. Ozsváth and Z. Szabó on a 4-manifold $M$ with a nonzero Seiberg-Witten invariant for a Spin${}^c$ structure $\mathfrak{s}$, when an embedded surface $\Sigma \subset M$ satisfies $[\Sigma ]\cdot [\Sigma ]\ge 0$ and $$|⟨[\Sigma ],c_1(\mathfrak{s})⟩|+[\Sigma ]\cdot [\Sigma ]\ge 2b_1(M).$$