On cohomology of almost complex 4-manifolds
Qiang Tan, Hongyu Wang, Ying Zhang, and Peng Zhu

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.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric and Algebraic Topology · Geometric Analysis and Curvature Flows
