Abstract
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We define and study the symplectic semi-characteristic of a closed
-dimensional
symplectic manifold, based on the even-degree part of the primitive cohomology.
Using a vector field with nondegenerate zero points, we prove a counting
formula for the symplectic semi-characteristic. 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 choice of symplectic
forms.
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Keywords
mod 2 index, primitive cohomology, symplectic
semi-characteristic
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Mathematical Subject Classification
Primary: 58J20
Secondary: 53D05
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Milestones
Received: 30 October 2025
Revised: 10 March 2026
Accepted: 21 April 2026
Published: 22 May 2026
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| © 2026 MSP (Mathematical Sciences
Publishers). Distributed under the Creative Commons
Attribution License 4.0 (CC BY). |
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