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Classification of compact homogeneous spaces with invariant symplectic structures

Author: Daniel Guan
Journal: Electron. Res. Announc. Amer. Math. Soc. 3 (1997), 52-54
MSC (1991): Primary 53C15, 57S25, 53C30; Secondary 22E99, 15A75
Published electronically: July 29, 1997
MathSciNet review: 1464575
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Abstract: We solve a longstanding problem of classification of compact homogeneous spaces with invariant symplectic structures. We also give a splitting conjecture on compact homogeneous spaces with symplectic structures (which are not necessarily invariant under the group action) that makes the classification of this kind of manifolds possible.

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Additional Information

Daniel Guan
Affiliation: Department of Mathematics, Princeton University, Princeton, NJ 08544

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): February 21, 1997
Published electronically: July 29, 1997
Additional Notes: Supported by NSF Grant DMS-9401755 and DMS-9627434.
Communicated by: Gregory Margulis
Article copyright: © Copyright 1997 American Mathematical Society