On cohomology of almost complex 4-manifolds

TL;DR

This paper investigates the properties of the J-anti-invariant cohomology subgroup in almost Hermitian 4-manifolds, showing that for generic structures, this subgroup's dimension is zero, advancing understanding of their cohomological features.

Contribution

It proves that the dimension of the J-anti-invariant cohomology subgroup is zero for generic almost complex structures on 4-manifolds, extending recent work in the field.

Findings

h_J = 0 for generic J on M

Advances understanding of cohomological properties of almost complex structures

Builds on recent work by Draghici, Li, and Zhang

Abstract

Based on recent work of T. Draghici, T.-J. Li and W. Zhang, we further investigate properties of the dimension h_J of the J-anti-invariant cohomology subgroup H_J of a closed almost Hermitian 4-manifold (M, g, J, F) using metric compatible and symplectic 2-form compatible almost complex structures. We prove that h_J = 0 for generic almost complex structures J on M.