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Anglický jazyk
EQUIVARIANT SYMPLECTIC HODGE THEORY AND STRONG LEFSCHETZ MANIFOLDS
Autor: Yi Lin
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 dd-lemma, and an improved version of the Kirwan-Ginzburg equivariant... Viac o knihe
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O knihe
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 dd-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 dd-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.
- Vydavateľstvo: LAP LAMBERT Academic Publishing
- Rok vydania: 2009
- Formát: Paperback
- Rozmer: 220 x 150 mm
- Jazyk: Anglický jazyk
- ISBN: 9783838318356
