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 applications of this machinery (including the study of Poisson cohomology), and study specific examples of a few of them in depth.

arXiv comment19 pages

Cited by in corpus (10)

• Reduction theory for singular symplectic manifolds and singular forms on moduli spaces
• $b$-Structures on Lie groups and Poisson reduction
• Singular cotangent models and complexity in fluids with dissipation
• On the singular Weinstein conjecture and the existence of escape orbits for $b$-Beltrami fields
• Hamiltonian facets of classical gauge theories on $E$-manifolds
• Stability of fixed points of Dirac structures
• The Arnold conjecture for singular symplectic manifolds
• Non-exactness of toric Poisson structures
• E-structures and almost regular Poisson manifolds
• A counterexample to the singular Weinstein conjecture