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 $b_1=0$. We demonstrate that the inequality is especially powerful when $2\tilde{\chi }+3\sigma \ge 0$, where $\tilde{\chi }$ is the modified Euler number taking account of the cup product on $H^1$.

23 pages, accepted for publication by the Journal of Topology

Cited by in corpus (2)

• Bounds on genus and configurations of embedded surfaces in 4-manifolds
• The Minimal Genus Problem