A Serre type vanishing property of the twisted primitive cohomology

2026/05/20 by Hao Zhuang · 1 voice
Mathematics · #math.SG #math.DG

paper · pdf

Abstract

We prove a Serre type vanishing property for the twisted primitive cohomology of a symplectic manifold. It is based on Tseng and Zhou's vanishing property under the symplectic flatness. These vanishing properties emphasizes the necessity of the symplectic flatness when generalizing certain results from the sheaf cohomology in complex geometry to the primitive cohomology in symplectic geometry.

Citations

• Mapping Cone Connections and their Yang-Mills Functional
• Symplectically Flat Connections and Their Functionals
• Dolbeault cohomology for almost complex manifolds
• Differential Geometry
• Odd sphere bundles, symplectic manifolds, and their intersection theory
• Cohomology and Hodge Theory on Symplectic Manifolds: I
• Heat Kernels and Dirac Operators

Discussions

• Hao Zhuang: A Serre type vanishing property of the twisted primitive cohomology https://arxiv.org/abs/2605.21410 https://arxiv.org/pdf/2605.21410 https://arxiv.org/html/2605.21410 [bsky, 0 points, 0 comments]

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