Irreducible 4-manifolds with abelian non-cyclic fundamental group of small rank

TL;DR

This paper constructs numerous irreducible symplectic 4-manifolds with abelian non-cyclic fundamental groups and explores the classification of manifolds with finite non-cyclic fundamental groups.

Contribution

It introduces new examples of irreducible symplectic 4-manifolds with specific abelian non-cyclic fundamental groups and studies their classification.

Findings

Construction of many irreducible symplectic 4-manifolds with abelian non-cyclic fundamental groups

Analysis of the classification (botany) of manifolds with finite non-cyclic fundamental groups

Advancement in understanding the topology of 4-manifolds with complex fundamental groups

Abstract

A myriad of irreducible symplectic 4-manifolds with abelian non-cyclic fundamental group is constructed. The botany of manifolds with finite non-cyclic fundamental groups is also studied.