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## Classification of compact homogeneous spaces with
invariant symplectic structures

### Daniel Guan

**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.

*Copyright 1997 American Mathematical Society*

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#### Article Info

- ERA Amer. Math. Soc.
**03** (1997), pp. 52-54
- Publisher Identifier: S 1079-6762(97)00023-1
- 1991
*Mathematics Subject Classification*. Primary 53C15, 57S25, 53C30; Secondary 22E99, 15A75
*Key words and phrases*. 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 the editors February 21, 1997
- Posted on July 29, 1997
- Communicated by Gregory Margulis
- Comments (When Available)

**Daniel Guan**

Department of Mathematics, Princeton University, Princeton, NJ 08544

*E-mail address:* `zguan@math.princeton.edu`

Supported by NSF Grant DMS-9401755 and DMS-9627434.

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