$\hat{I}¸$-almost twisted Poisson cohomology

Abstract

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

20 pages