$\theta$-almost twisted Poisson cohomology

Nasser Saipele Nansidi; Bertuel Tangue Ndawa; Joseph Dongho

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arXiv · 2502.18503

$\theta$-almost twisted Poisson cohomology

Nasser Saipele Nansidi·Bertuel Tangue Ndawa·Joseph Dongho

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Abstract

We introduce the notion of a $\theta$-almost twisted Poisson structure on manifolds, which involves incorporating a closed $1$-form $\theta$ 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 $\theta$-almost twisted Poisson cohomology. An example illustrating this cohomology is also presented on $\mathbb{R}^5$.

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Nasser Saipele Nansidi, Bertuel Tangue Ndawa, Joseph Dongho. 2025-02-21. $\theta$-almost twisted Poisson cohomology. https://arxiv.org/abs/2502.18503

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