Primitive cohomology of degree 2 on compact symplectic manifolds

2014/03/08 by Qiang Tan, Hongyu Wang, Tan, Qiang +3 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1403.1963

openalex publication_date 2014/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we define the generalized Lejmi's P_J operator on a compact almost Kähler 2n-manifold. We get that J is C^∞-pure and full if dimker P_J=b²-1. Additionally, we investigate the relationship between J-anti-invariant cohomology introduced by T.-J. Li and W. Zhang and new symplectic cohomologies introduced by L.-S. Tseng and S.-T. Yau on a closed symplectic 4-manifold.

Citations

• Symplectic Harmonic theory and the Federer-Fleming deformation theorem

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

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