A note on the deformations of almost complex structures on compact four-manifolds

2014/11/15 by Qiang Tan, Hongyu Wang, Tan, Qiang +3
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1411.4103

openalex publication_date 2014/11/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we calculate the dimension of the J-anti-invariant cohomology subgroup H_J^- on \mathbbT⁴. Inspired by the concrete example, \mathbbT⁴, we get that: On a closed symplectic 4-dimensional manifold (M, ω), h^-_J=0 for generic ω-compatible almost complex structures.

Citations

• Primitive cohomology of degree 2 on compact symplectic manifolds

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• On the J-anti-invariant cohomology of almost complex 4-manifolds
• Symplectic Cohomology and the Stability of J-Anti-Invariant Cohomology
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