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Modification and the cohomology groups of compact solvmanifolds
Author(s):
Daniel
Guan
Journal:
Electron. Res. Announc. Amer. Math. Soc.
13
(2007),
74-81.
MSC (2000):
Primary 53C15, 57S25, 53C30, 22E99, 15A75
Posted:
December 7, 2007
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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.
References:
-
- [Dm]
- J. Dorfmeister: Homogeneous Kähler Manifolds Admitting a Transitive Solvable Group of Automorphisms, Ann. Scient. Ec. Norm. Sup., 4 Ser., 18 (1985), 143-180. MR 803198 (87j:32094)
- [DN]
- J. Dorfmeister & K. Nakajima: The Fundamental Conjecture for Homogeneous Kähler Manifolds, Acta Math. 161 (1988), 23-70. MR 962095 (89i:32066)
- [DG]
- J. Dorfmeister & Z.-D. Guan: Classification of Compact Homogeneous Pseudo-Kähler Manifolds, Comment. Math. Helv. 67 (1992), 499-513. MR 1185806 (93i:32042)
- [Gb1]
- V. V. Gorbatsevich: Splittings of Lie Groups and Their Application to the Study of Homogeneous Spaces, Math. USSR Izv. 15 (1979), 441-467. MR 0567035 (82e:22019)
- [Gb2]
- V. V. Gorbatsevich: Plesiocompact Homogeneous Spaces, Siber. Math. J. 30 (1989), 217-226. MR 997468 (90f:22010)
- [Gu1]
- Z. Guan: Examples of compact holomorphic symplectic manifolds which admit no Kähler structure. In Geometry and Analysis on Complex Manifolds--Festschrift for Professor S. Kobayashi's 60th Birthday, World Scientific 1994, pp. 63-74. MR 1463964 (98h:53109)
- [Gu2]
- D. Guan: A Splitting Theorem for Compact Complex Homogeneous Spaces with a Symplectic Structure, Geom. Dedi. 67 (1996), 217-225. MR 1413633 (98a:53105)
- [Gu3]
- D. Guan: On Compact Symplectic Manifolds with Lie Group Symmetries, Transactions of AMS 357 (2005), 3359-3373. MR 2135752 (2006c:53094)
- [Gu4]
- D. Guan: Classification of Compact Complex Homogeneous Manifolds with Pseudo-Kählerian Structures, Preprint, 2007.
- [Hk]
- A. Huckleberry: Homogeneous Pseudo-Kählerian Manifolds: A Hamiltonian Viewpoint, Note Mat. 10 (1990), 337-342. MR 1221949 (94f:53052)
- [Rg]
- M. S. Raghunathan: Discrete Subgroups of Lie Groups, Springer-Verlag, Berlin, 1972. MR 0507234 (58:22394a)
- [Ym]
- T. Yamada: A Pseudo-Kähler Structure on a Nontoral Compact Complex Parallelizable Solvmanifold, Geom. Dedicata 112 (2005), 115-122. MR 2163892 (2006e:53061)
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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
DOI:
10.1090/S1079-6762-07-00176-X
PII:
S 1079-6762(07)00176-X
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
Posted:
December 7, 2007
Communicated by:
Keith Burns
Copyright of article:
Copyright
2007,
American Mathematical Society
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