Geography of spin symplectic 4-manifolds with abelian fundamental group

TL;DR

This paper extends the classification and construction techniques of symplectic 4-manifolds from simply connected cases to those with abelian fundamental groups, using Luttinger surgeries.

Contribution

It re-proves and extends results on symplectic 4-manifolds to include non-simply connected cases with abelian fundamental groups.

Findings

Extended classification to non-simply connected manifolds

Applied Luttinger surgeries to construct new examples

Re-proved key results for simply connected cases

Abstract

In this paper, results of J. Park and of B.D Park and Szabo on simply connected symplectic 4-manifolds are re-proven and extended to non-simply connected manifolds using Luttinger surgeries.