$θ$-almost twisted Poisson cohomology
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911149526614016 |
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| author | Nansidi, Nasser Saipele Ndawa, Bertuel Tangue Dongho, Joseph |
| author_facet | Nansidi, Nasser Saipele Ndawa, Bertuel Tangue Dongho, Joseph |
| contents | We introduce the notion of a $θ$-almost twisted Poisson structure on manifolds, which involves incorporating a closed $1$-form $θ$ into twisted Poisson structures under specific conditions. We provide a characterization of this structure on low-dimensional manifolds and construct the Lie-Rinehart algebra on the module of $1$-forms on manifolds equipped with this structure. This construction leads to a cochain complex and its associated cohomology, which we refer to as $θ$-almost twisted Poisson cohomology. An example illustrating this cohomology is also presented on $\mathbb{R}^5$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18503 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $θ$-almost twisted Poisson cohomology Nansidi, Nasser Saipele Ndawa, Bertuel Tangue Dongho, Joseph Differential Geometry We introduce the notion of a $θ$-almost twisted Poisson structure on manifolds, which involves incorporating a closed $1$-form $θ$ into twisted Poisson structures under specific conditions. We provide a characterization of this structure on low-dimensional manifolds and construct the Lie-Rinehart algebra on the module of $1$-forms on manifolds equipped with this structure. This construction leads to a cochain complex and its associated cohomology, which we refer to as $θ$-almost twisted Poisson cohomology. An example illustrating this cohomology is also presented on $\mathbb{R}^5$. |
| title | $θ$-almost twisted Poisson cohomology |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2502.18503 |