EQUIVARIANT SYMPLECTIC HODGE THEORY AND STRONG LEFSCHETZ MANIFOLDS
Yi Lin
Broschiertes Buch

EQUIVARIANT SYMPLECTIC HODGE THEORY AND STRONG LEFSCHETZ MANIFOLDS

A study of Hamiltonian symplectic geometry from a Hodge theoretic point of view

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Consider the Hamiltonian action of a compact Lie group on a symplectic manifold which has the strong Lefschetz property. We first establish an equivariant version of the Merkulov-Guillemin d -lemma, and an improved version of the Kirwan-Ginzburg equivariant formality theorem, which says that every cohomology class has a canonical equivariant extension. We then proceed to extend the equivariant d -lemma to equivariant differential forms with generalized coefficients. Finally we investigate the subtle differences between an equivariant Kaehler manifold and a Hamiltonian symplectic manifold with ...