Equivariant symplectic Hodge theory and the $d_Gδ$-lemma

Mathematics – Symplectic Geometry

Scientific paper

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10 pages

Scientific paper

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 $d\delta$-lemma and an improved version of the
Kirwan-Ginzburg equivariant formality theorem, which says that every cohomology
class has a \emph{canonical} equivariant extension.

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