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arXiv · 2505.14496

Symplectic semi-characteristics

Hao Zhuang
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Abstract

We study the symplectic semi-characteristic of a closed 4n-dimensional symplectic manifold. First, using the even-degree part of the primitive cohomology, we define the symplectic semi-characteristic. Second, using a vector field with nondegenerate zero points, we prove a counting formula for the symplectic semicharacteristic. As corollaries of the counting formula, we obtain a vanishing property and the fact that the definition of the symplectic semi-characteristic is independent of the choices of symplectic forms.

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Hao Zhuang. 2025-05-20. Symplectic semi-characteristics. https://doi.org/10.2140/pjm.2026.343.485

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