{"product_id":"equivariant-symplectic-hodge-theory-and-strong-lefschetz-manifolds-von-yi-lin","title":"EQUIVARIANT SYMPLECTIC HODGE THEORY AND STRONG LEFSCHETZ MANIFOLDS","description":"\u003cp\u003eConsider 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 the strong  Lefscehtz property. Among other things, we construct six-dimensional compact non-Kaehler  Hamiltonian circle manifolds which each satisfy the  Hard Lefschetz property, but nevertheless each have  a symplectic quotient which does not satisfy the  strong Lefschetz property. As an aside we prove that  the strong Lefschetz property, unlike that of  equivariant Kaehler condition, does not guarantee  the Duistermaat-Heckman function to be log-concave.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783838318356\"\u003e\u003ch3\u003eA study of Hamiltonian symplectic geometry from a Hodge theoretic point of view\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783838318356","offer_id":39497038331997,"sku":"9783838318356","price":49.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/eeb31852-e557-4b4e-9b3f-34716ffb3c0d.jpg?v=1757825962","url":"https:\/\/shop.autorenwelt.de\/products\/equivariant-symplectic-hodge-theory-and-strong-lefschetz-manifolds-von-yi-lin","provider":"Autorenwelt Shop","version":"1.0","type":"link"}