On the topology of~non-compact simply~connected homogeneous manifolds
Izvestiya. Mathematics , Tome 84 (2020) no. 5, pp. 845-861.

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

We study the covariant bundles (Mostow bundles) for simply connected homogeneous manifolds, establish their relation to homogeneous bundles and consider classes of homogeneous manifolds for which the Mostow bundle is trivial (resp. non-trivial). We also give a classification of non-compact simply connected homogeneous manifolds of dimension not exceeding seven.
Keywords: homogeneous manifold, covariant bundle, homogeneous bundle, Mostow bundle, topological triviality of a bundle.
@article{IM2_2020_84_5_a1,
     author = {V. V. Gorbatsevich},
     title = {On the topology of~non-compact simply~connected homogeneous manifolds},
     journal = {Izvestiya. Mathematics },
     pages = {845--861},
     publisher = {mathdoc},
     volume = {84},
     number = {5},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2020_84_5_a1/}
}
TY  - JOUR
AU  - V. V. Gorbatsevich
TI  - On the topology of~non-compact simply~connected homogeneous manifolds
JO  - Izvestiya. Mathematics 
PY  - 2020
SP  - 845
EP  - 861
VL  - 84
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2020_84_5_a1/
LA  - en
ID  - IM2_2020_84_5_a1
ER  - 
%0 Journal Article
%A V. V. Gorbatsevich
%T On the topology of~non-compact simply~connected homogeneous manifolds
%J Izvestiya. Mathematics 
%D 2020
%P 845-861
%V 84
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2020_84_5_a1/
%G en
%F IM2_2020_84_5_a1
V. V. Gorbatsevich. On the topology of~non-compact simply~connected homogeneous manifolds. Izvestiya. Mathematics , Tome 84 (2020) no. 5, pp. 845-861. http://geodesic.mathdoc.fr/item/IM2_2020_84_5_a1/

[1] G. D. Mostow, “The extensibility of local Lie groups of transformations and groups on surfaces”, Ann. of Math. (2), 52:3 (1950), 606–636 | DOI | MR | Zbl

[2] V. V. Gorbatsevich, “Three-dimensional homogeneous spaces”, Siberian Math. J., 18:2 (1977), 200–210 | DOI | MR | Zbl

[3] V. V. Gorbatsevich, A. L. Onishchik, “Lie transformation groups”, Lie groups and Lie algebras, v. I, Encyclopaedia Math. Sci., 20, Springer, Berlin, 1993, 95–235 | MR | MR | Zbl | Zbl

[4] G. D. Mostow, “On covariant fiberings of Klein spaces”, Amer. J. Math., 77:2 (1955), 247–278 | DOI | MR | Zbl

[5] G. D. Mostow, “On covariant fiberings of Klein spaces. II”, Amer. J. Math., 84:3 (1962), 466–474 | DOI | MR | Zbl

[6] F. I. Karpelevich, “O rassloenii odnorodnykh prostranstv”, UMN, 11:3(69) (1956), 131–138 | MR | Zbl

[7] A. L. Onishchik, Topology of transitive transformation groups, Johann Ambrosius Barth Verlag GmbH, Leipzig, 1994, xvi+300 pp. | MR | MR | Zbl | Zbl

[8] T. Kaga, T. Watabe, “Simply connected 6-manifolds of large degree of symmetry”, Sci. Rep. Niigata Univ. Ser. A, 1975, no. 12, 15–32 | MR | Zbl

[9] S. Klaus, Einfach-zusammenhängende kompakte homogene Räume bis zur dimension Neun, Diploma thesis, Mainz Univ., Mainz, 1988, 97 pp. | DOI

[10] D. B. Fuks, V. A. Rokhlin, Beginner's course in topology. Geometric chapters, Universitext, Springer-Verlag, Berlin, 1984, xi+519 pp. | MR | MR | Zbl | Zbl

[11] V. V. Gorbatsevich, “On a fibration of compact homogeneous spaces”, Trans. Mosc. Math. Soc., 1983, no. 1, 129–157 | MR | Zbl

[12] V. V. Gorbacevič, “On a class of decompositions of semisimple Lie groups and algebras”, Math. USSR-Sb., 24:2 (1974), 287–297 | DOI | MR | Zbl

[13] C. Chevalley, Theory of Lie groups, v. I, Princeton Math. Ser., 8, Princeton Univ. Press, Princeton, NJ, 1946, ix+217 pp. | MR | Zbl

[14] M. A. Naimark, A. I. Stern, Theory of group representations, Grundlehren Math. Wiss., 246, Springer-Verlag, New York, 1982, ix+568 pp. | MR | MR | Zbl | Zbl

[15] R. W. Brockett, H. J. Sussmann, “Tangent bundles of homogeneous spaces are homogeneous spaces”, Proc. Amer. Math. Soc., 35:2 (1972), 550–551 | DOI | MR | Zbl

[16] V. V. Gorbatsevich, “O pochti odnorodnykh prostranstvakh”, Geometricheskie metody v zadachakh analiza i algebry, 1, Izd-vo YarGU, Yaroslavl, 1978, 43–66 | MR | Zbl

[17] W. Browder, J. Levine, G. R. Livesay, “Finding a boundary for an open manifold”, Amer. J. Math., 87:4 (1965), 1017–1028 | DOI | MR | Zbl

[18] J. Milnor, “Whitehead torsion”, Bull. Amer. Math. Soc., 72:3 (1966), 358–426 | DOI | MR | Zbl

[19] B. Hughes, A. A. Ranicki, Ends of complexes, Cambridge Tracts in Math., 123, Reprint of 1996 ed., Cambridge Univ. Press, Cambridge, 2008, xxv+353 pp. | MR | Zbl

[20] W. Massey, “On the cohomology ring of a sphere bundle”, J. Math. Mech., 7:2 (1958), 265–289 | DOI | MR | Zbl

[21] P. L. Antonelly, D. Burghelea, P. J. Kahn, “The non-finite homotopy type of some diffeomorphism groups”, Topology, 11 (1972), 1–49 | DOI | MR | Zbl

[22] R. Mandelbaum, Chetyrekhmernaya topologiya, Mir, M., 1981, 288 pp. | MR | Zbl

[23] A. Dold, H. Whitney, “Classification of oriented sphere bundles over a 4-complex”, Ann. of Math. (2), 69:3 (1959), 667–677 | DOI | MR | Zbl

[24] D. Barden, “Simply connected five-manifolds”, Ann. of Math. (2), 82:3 (1965), 365–385 | DOI | MR | Zbl