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Modification and the cohomology groups of compact solvmanifolds

Author: Daniel Guan
Journal: Electron. Res. Announc. Amer. Math. Soc. 13 (2007), 74-81
MSC (2000): Primary 53C15, 57S25, 53C30, 22E99, 15A75
Published electronically: December 7, 2007
MathSciNet review: 2358304
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Abstract: In this note we give a modification theorem for a compact homogeneous solvmanifold such that a certain Mostow type condition will be satisfied. An application of this result is a simpler way to calculate the cohomology groups of compact quotients of real solvable Lie group over a cocompact discrete subgroup. Furthermore, we apply the second result to obtain a splitting theorem for compact complex homogeneous manifolds with symplectic structures. In particular, we are able to classify compact complex homogeneous spaces with pseudo-Kählerian structures.

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Additional Information

Daniel Guan
Affiliation: Department of Mathematics, University of California at Riverside, Riverside, CA 92507

Keywords: Solvmanifolds, cohomology, invariant structure, homogeneous space, product, fiber bundles, symplectic manifolds, splittings, prealgebraic group, decompositions, modification, Lie group, compact manifolds, uniform discrete subgroups, locally flat parallelizable manifolds
Received by editor(s): August 10, 2006
Published electronically: December 7, 2007
Communicated by: Keith Burns
Article copyright: © Copyright 2007 American Mathematical Society

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