The fundamental group of symplectic $4$-manifolds with $b^{+}=1$

Abstract

In this article we apply the technique of Luttinger surgery to study the complexity of the fundamental group of symplectic $4$-manifolds with holomorphic Euler number ${\chi }_h=1$. We discuss the topology of symplectic $4$-manifolds with $b^{+}=1$ and provide various constructions of symplectic $4$-manifolds with $b^{+}=1$ and prescribed $c_1^2$.

34 pages, 6 figures. In this version, we revised the paper according to the comments and suggestions of the reviewers. Comments are welcome

Cited by in corpus (3)

• Moduli space of $J$-holomorphic subvarieties
• Genus two Lefschetz fibrations with $b_2^{+}=1$ and ${c_1}^2=1,2$
• The curve cone of almost complex 4-manifolds