This journal is archived by the American Mathematical Society. The master copy is available at http://www.ams.org/era/

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

TeX source (11K)
DVI (10K)
PostScript (66K)

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.