Homotopy moment maps

Understand

Associated to any manifold equipped with a closed form of degree >1 is an `L-infinity algebra of observables' which acts as a higher/homotopy analog of the Poisson algebra of functions on a symplectic manifold.

• In order to study Lie group actions on these manifolds, we introduce a theory of homotopy moment maps.
• Such a map is a L-infinity morphism from the Lie algebra of the group into the observables which lifts the infinitesimal action.
• We establish the relationship between homotopy moment maps and equivariant de Rham cohomology, and analyze the obstruction theory for the existence of such maps.