Transgression in the primitive cohomology
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911348072382464 |
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| author | Zhuang, Hao |
| author_facet | Zhuang, Hao |
| contents | We study the Chern-Weil theory for the primitive cohomology of a symplectic manifold. First, given a symplectic manifold, we review the superbundle-valued forms on this manifold and prove a primitive version of the Bianchi identity. Second, as the main result, we prove a transgression formula associated with the boundary map of the primitive cohomology. Third, as an application of the main result, we introduce the concept of primitive characteristic classes and point out a further direction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24920 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Transgression in the primitive cohomology Zhuang, Hao Differential Geometry Mathematical Physics Symplectic Geometry 57R20 (Primary) 53C05, 53D05 (Secondary) We study the Chern-Weil theory for the primitive cohomology of a symplectic manifold. First, given a symplectic manifold, we review the superbundle-valued forms on this manifold and prove a primitive version of the Bianchi identity. Second, as the main result, we prove a transgression formula associated with the boundary map of the primitive cohomology. Third, as an application of the main result, we introduce the concept of primitive characteristic classes and point out a further direction. |
| title | Transgression in the primitive cohomology |
| topic | Differential Geometry Mathematical Physics Symplectic Geometry 57R20 (Primary) 53C05, 53D05 (Secondary) |
| url | https://arxiv.org/abs/2512.24920 |