The geometry of E-manifolds

Abstract

Motivated by the study of symplectic Lie algebroids, we study a describe a type of algebroid (called an E-tangent bundle) which is particularly well-suited to study of singular differential forms and their cohomology. This setting generalizes the study of b-symplectic manifolds, foliated manifolds, and a wide class of Poisson manifolds. We generalize Moser's theorem to this setting, and use it to construct symplectomorphisms between singular symplectic forms. We give appli- cations of this machinery (including the study of Poisson cohomology), and study specific examples of a few of them in depth.