Complex and Symplectic Structures on Panelled Web 4-Manifolds

TL;DR

This paper investigates the symplectic and complex structures on panelled web 4-manifolds, providing new examples of almost complex manifolds that are neither symplectic nor complex, especially in non-simply connected cases.

Contribution

It introduces an infinite family of non-simply connected 4-manifolds that are almost complex but lack symplectic and complex structures.

Findings

Existence of infinite families of almost complex, non-symplectic, non-complex 4-manifolds

Examples specifically in the non-simply connected category

Insights into the structure of panelled web 4-manifolds

Abstract

We analyze the symplectic and complex structures on the panelled web 4-manifolds. In particular, we give infinite family of examples of almost complex but not symplectic and not complex 4-manifolds in the non-simply connected case.