Geodesic
Modification and the cohomology groups of compact solvmanifolds
Guan, Daniel1
1 Department of Mathematics, University of California at Riverside, Riverside, CA 92507
Electronic research announcements of the American Mathematical Society, Tome 13 (2007), pp. 74-81.

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S1079-6762-07-00176-X

Guan, Daniel 1

1 Department of Mathematics, University of California at Riverside, Riverside, CA 92507 
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Guan, Daniel. Modification and the cohomology groups of compact solvmanifolds. Electronic research announcements of the American Mathematical Society, Tome 13 (2007), pp. 74-81. doi : 10.1090/S1079-6762-07-00176-X. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-07-00176-X/

[1] Dorfmeister, Josef Homogeneous Kähler manifolds admitting a transitive solvable group of automorphisms Ann. Sci. École Norm. Sup. (4) 1985 143 180

[2] Dorfmeister, Josef, Nakajima, Kazufumi The fundamental conjecture for homogeneous Kähler manifolds Acta Math. 1988 23 70

[3] Dorfmeister, Josef, Guan, Zhuang Dan Classification of compact homogeneous pseudo-Kähler manifolds Comment. Math. Helv. 1992 499 513

[4] Gorbacevič, V. V. Decomposition of Lie groups and its applications to the study of homogeneous spaces Izv. Akad. Nauk SSSR Ser. Mat. 1979 1227 1258

[5] Gorbatsevich, V. V. Plesio-compact homogeneous spaces Sibirsk. Mat. Zh. 1989

[6] Guan, Daniel Examples of compact holomorphic symplectic manifolds which admit no Kähler structure 1994 63 74

[7] Guan, Daniel A splitting theorem for compact complex homogeneous spaces with a symplectic structure Geom. Dedicata 1996 217 225

[8] Guan, Daniel On compact symplectic manifolds with Lie group symmetries Trans. Amer. Math. Soc. 2005 3359 3373

[9] Huckleberry, A. T. Homogeneous pseudo-Kählerian manifolds: a Hamiltonian viewpoint Note Mat. 1990 337 342

[10] Raghunathan, M. S. Discrete subgroups of Lie groups 1972

[11] Yamada, Takumi A pseudo-Kähler structure on a nontoral compact complex parallelizable solvmanifold Geom. Dedicata 2005 115 122

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