Equivariant symplectic Hodge theory and the dGδ-lemma

Abstract

Consider a Hamiltonian action of a compact Lie group on a symplectic manifold which has the strong Lefschetz property. We establish an equivariant version of the Merkulov- Guillemin dδ-lemma and an improved version of the Kirwan- Ginzburg equivariant formality theorem, which says that every cohomology class has a canonical equivariant extension.