Geodesic
On the homotopy structure of compact complex homogeneous manifolds
Izvestiya. Mathematics , Tome 80 (2016) no. 2, pp. 329-341.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider compact complex homogeneous manifolds up to finite coverings. We give sufficient conditions under which the natural bundle for such a manifold is homotopically trivial. This triviality always holds in the case when the stationary subgroup is discrete.
Keywords: homogeneous space, lattice
Mots-clés : complex Lie group, homotopy type. 
@article{IM2_2016_80_2_a3,
     author = {V. V. Gorbatsevich},
     title = {On the homotopy structure of compact complex homogeneous manifolds},
     journal = {Izvestiya. Mathematics },
     pages = {329--341},
     publisher = {mathdoc},
     volume = {80},
     number = {2},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2016_80_2_a3/}
}
TY  - JOUR
AU  - V. V. Gorbatsevich
TI  - On the homotopy structure of compact complex homogeneous manifolds
JO  - Izvestiya. Mathematics 
PY  - 2016
SP  - 329
EP  - 341
VL  - 80
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2016_80_2_a3/
LA  - en
ID  - IM2_2016_80_2_a3
ER  - 
%0 Journal Article
%A V. V. Gorbatsevich
%T On the homotopy structure of compact complex homogeneous manifolds
%J Izvestiya. Mathematics 
%D 2016
%P 329-341
%V 80
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2016_80_2_a3/
%G en
%F IM2_2016_80_2_a3
V. V. Gorbatsevich. On the homotopy structure of compact complex homogeneous manifolds. Izvestiya. Mathematics , Tome 80 (2016) no. 2, pp. 329-341. http://geodesic.mathdoc.fr/item/IM2_2016_80_2_a3/

[1] E. B. Vinberg, V. V. Gorbatsevich, O. V. Shvartsman, “Discrete subgroups of Lie groups”, Lie groups and Lie algebras II, Encyclopaedia Math. Sci., 21, Springer, Berlin, 2000, 1–123 | MR | Zbl

[2] V. V. Gorbatsevich, “Some homotopy properties of the natural fibration for compact homogeneous manifolds”, Soviet Math. Dokl., 25 (1982), 657–661 | MR | Zbl

[3] V. V. Gorbatsevich, “On the triviality of natural bundles of some compact homogeneous spaces”, Russian Math. (Iz. VUZ), 44:1 (2000), 13–17 | MR | Zbl

[4] V. V. Gorbatsevich, “O kogomologiyakh kompaktnykh odnorodnykh prostranstv s diskretnoi statsionarnoi podgruppoi”, Voprosy teorii grupp i gomologicheskoi algebry, Izd-vo YarGU, Yaroslavl, 1990, 107–123 | MR | Zbl

[5] V. V. Gorbatsevich, A. L. Onishchik, “Lie transformation groups”, Lie groups and Lie algebras I, Encyclopaedia Math. Sci., 20, Springer, Berlin, 1993, 95–229 | MR | Zbl

[6] I. Chatterji, G. Mislin, Ch. Pittet, Flat bundles with complex analytic holonomy, arXiv: 1308.1412

[7] P. Deligne, D. Sullivan, “Fibres vectoriels complexes à groupe structural discret”, C. R. Acad. Sci. Paris Sér. A-B, 281:24 (1975), 1081–1083 | MR | Zbl

[8] V. V. Gorbatsevich, “On a fibration of compact homogeneous spaces”, Trans. Mosc. Math. Soc., 1983, No1, Amer. Math. Soc., Providence, RI, 1983, 129–157 | MR | Zbl

[9] M. Otte, J. Potters, “Beispiele homogener Mannigfaltigkeiten”, Manuscripta Math., 10:2 (1973), 117–127 | DOI | MR | Zbl

[10] V. I. Chernousov, “On the Hasse principle for groups of type $E_8$”, Soviet Math. Dokl., 39:3 (1989), 592–596 | MR | Zbl

[11] D. Guan, “Toward a classification of compact complex homogeneous spaces”, J. Algebra, 273:1 (2004), 33–59 | DOI | MR | Zbl

[12] G. D. Mostow, “On the topology of homogeneous spaces of finite measure”, Convegno sui gruppi topologici e gruppi di Lie (INDAM, Roma, Gennaio, 1974), Symposia Mathematica, 16, Academic Press, London, 1975, 375–398 | MR | Zbl

[13] V. V. Gorbatsevich, “Modifikatsii tranzitivnykh deistvii grupp Li na kompaktnykh mnogoobraziyakh i ikh primeneniya”, Voprosy teorii grupp i gomologicheskoi algebry, Izd-vo YarGU, Yaroslavl, 1981, 131–145 | MR | Zbl

[14] D. N. Ahiezer, “Compact complex homogeneous spaces with solvable fundamental group”, Math. USSR-Izv., 8:1 (1974), 61–83 | DOI | MR | Zbl