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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
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
Published electronically: 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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Additional Information

Daniel Guan
Affiliation: Department of Mathematics, University of California–Riverside, Riverside, California 92521
Email: zguan@math.ucr.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-05-03657-3
PII: S 0002-9947(05)03657-3
Keywords: Invariant structure, homogeneous space, product, fiber bundles, symplectic manifolds, splittings, prealgebraic group, decompositions, modification, Lie group, symplectic algebra, compact manifolds, uniform discrete subgroups, classifications, locally flat parallelizable manifolds
Received by editor(s): May 22, 2002
Received by editor(s) in revised form: February 26, 2004
Published electronically: March 10, 2005
Additional Notes: This work was supported by NSF Grant DMS-9627434 and DMS-0103282
Article copyright: © Copyright 2005 American Mathematical Society