Bounds on genus and configurations of embedded surfaces in 4-manifolds

Abstract

For several embedded surfaces with zero self-intersection number in 4-manifolds, we show that an adjunction-type genus bound holds for at least one of the surfaces under certain conditions. For example, we derive certain adjunction inequalities for surfaces embedded in $m{\mathbb{CP}}^2\#n(-{\mathbb{CP}}^2)$ ($m,n\ge 2$). The proofs of these results are given by studying a family of Seiberg-Witten equations.

25pages, 2figures. v3: Section 2 is divided into two parts: Subsection 2.1 and Subsection 2.2

References in corpus (1)

• Minimal genus for 4-manifolds with $b^{+}=1$

Cited by in corpus (4)

• Obstructions to smooth group actions on 4-manifolds from families Seiberg-Witten theory
• Characteristic classes via 4-dimensional gauge theory
• Positive scalar curvature and higher-dimensional families of Seiberg-Witten equations
• The Minimal Genus Problem