The geometry of \(E\)-manifolds (Q2031511)

From the abstract: ``Motivated by the study of symplectic Lie algebroids, we focus on a type of algebroid (called an \(E\)-tangent bundle) which is particularly well-suited to the study of singular differential forms and their cohomology. This setting generalizes \(b\)-symplectic manifolds, foliated manifolds, and a wide class of Poisson manifolds.'' Moreover, a counterexample to the classical Darboux theorem in this setting is given. The \(E\)-cohomology is studied as well. The authors give an example of an \(E\)-tangent bundle whose \(E\)-cohomology is not isomorphic to the Poisson cohomology.