Poisson geometry with a 3-form background
arXiv:math/0107133
Abstract
We study a modification of Poisson geometry by a closed 3-form. Just as for ordinary Poisson structures, these "twisted" Poisson structures are conveniently described as Dirac structures in suitable Courant algebroids. The additive group of 2-forms acts on twisted Poisson structures and permits them to be seen as glued from ordinary Poisson structures defined on local patches. We conclude with remarks on deformation quantization and twisted symplectic groupoids.
10 pages, PTPTeX style; v2: minor changes, version to be published