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OverviewConsider 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 dδ-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 dδ-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. Full Product DetailsAuthor: Yi Lin (Slippery Rock University Pennsylvania USA)Publisher: LAP Lambert Academic Publishing Imprint: LAP Lambert Academic Publishing Dimensions: Width: 15.20cm , Height: 0.50cm , Length: 22.90cm Weight: 0.141kg ISBN: 9783838318356ISBN 10: 3838318358 Pages: 88 Publication Date: 02 June 2010 Audience: General/trade , General Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |