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
DOI:
https://doi.org/10.1090/S1079-6762-07-00176-X
Published electronically:
December 7, 2007
MathSciNet review:
2358304
Full-text PDF Free Access
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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
Email:
zguan@math.ucr.edu
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
