EQUIVARIANT SYMPLECTIC HODGE THEORY AND STRONG LEFSCHETZ MANIFOLDS: A study of Hamiltonian symplectic geometry from a Hodge theoretic point of view - Image 1

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LAP Lambert Academic Publishing EQUIVARIANT SYMPLECTIC HODGE THEORY AND STRONG LEFSCHETZ MANIFOLDS: A study of Hamiltonian symplectic geometry from a Hodge theoretic point of view

Name: EQUIVARIANT SYMPLECTIC HODGE THEORY AND STRONG LEFSCHETZ MANIFOLDS: A study of Hamiltonian symplectic geometry from a Hodge theoretic point of view
Brand: LAP Lambert Academic Publishing
Price: 44.0 GBP
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Geometry & Topology

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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 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.

Product Specifications

Brand: LAP Lambert Academic Publishing
Format: paperback
ASIN: 3838318358
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Geometry & Topology
Domain: Amazon UK
Release Date: 11 November 2009
Listed Since: 16 November 2009

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LAP Lambert Academic Publishing 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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