On compact symplectic manifolds with Lie group symmetries

Guan, Daniel

doi:10.1090/S0002-9947-05-03657-3

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ISSN 1088-6850(online) ISSN 0002-9947(print)

On compact symplectic manifolds with Lie group symmetries

Author: Daniel Guan
Journal: Trans. Amer. Math. Soc. 357 (2005), 3359-3373
MSC (2000): Primary 53C15, 57S25, 53C30, 22E99, 15A75
Posted: March 10, 2005
MathSciNet review: 2135752
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Abstract: In this note we give a structure theorem for a finite-dimensional subgroup of the automorphism group of a compact symplectic manifold. An application of this result is a simpler and more transparent proof of the classification of compact homogeneous spaces with invariant symplectic structures. We also give another proof of the classification from the general theory of compact homogeneous spaces which leads us to a splitting conjecture on compact homogeneous spaces with symplectic structures (which are not necessary invariant under the group action) that makes the classification of this kind of manifold possible.

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