Geodesic
Lattices in solvable Lie groups and deformations of homogeneous spaces
Sbornik. Mathematics, Tome 20 (1973) no. 2, pp. 249-266 Cet article a éte moissonné depuis la source Math-Net.Ru

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The space $\mathrm{SD}_n$ of pairs $(S,\Gamma)$ is studied, where $S$ is a solvable simply-connected Lie group and $\Gamma$ is a lattice in $S$, considered up to isomorphism. The structure of a neighborhood of a point $(S,\Gamma)\in\mathrm{SD}_n$ is described for two classes of groups $S$. In this connection deformations of homogeneous spaces are studied. Homogeneous spaces of type $K(\pi,1)$ are studied in the Appendix. Bibliography: 14 titles. 
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     title = {Lattices in solvable {Lie} groups and deformations of homogeneous spaces},
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V. V. Gorbatsevich. Lattices in solvable Lie groups and deformations of homogeneous spaces. Sbornik. Mathematics, Tome 20 (1973) no. 2, pp. 249-266. http://geodesic.mathdoc.fr/item/SM_1973_20_2_a3/

[1] L. Auslender, L. Grin, F. Khan, Potoki na odnorodnykh prostranstvakh, izd-vo «Mir», Moskva, 1966 | MR

[2] W. Barth, M. Otte, “Über fast-uniforme Üntergruppen komplexer Liegruppen und auslösbare komplexe Mannigfaltigkeiten”, Comm. Math. Helv., 44:3 (1969), 269–281 | DOI | MR | Zbl

[3] K. Shevalle, Teoriya grupp Li, t. I, IL, Moskva, 1948; т. II, ИЛ, Москва, 1958

[4] P. Conner, D. Montgomery, “Transformation groups on $K(\pi, 1)$”, Michigan Math. J., 6:4 (1969), 405–412 | MR

[5] H. Garland, M. Goto, “Lattices and the adjoint group of a Lie group”, Trans. Amer. Math. Soc., 124:3 (1966), 450–460 | DOI | MR | Zbl

[6] V. V. Gorbatsevich, “Diskretnye podgruppy razreshimykh grupp Li tipa $(\mathrm{E})$”, Matem. sb., 85 (127) (1971), 238–255 | Zbl

[7] A. I. Maltsev, “Ob odnom klasse odnorodnykh prostranstv”, Izv. AN SSSR, seriya matem., 13 (1949), 1–27

[8] G. Mostow, “Some applications of representative functions to solvmanifolds”, Amer. J. Math., 93:1 (1971), 11–32 | DOI | MR | Zbl

[9] G. M. Mubarakzyanov, “O razreshimykh algebrakh Li”, Izv. VUZov, 1963, no. 1, 114–123

[10] T. Nono, “Sur l'application exponentielle dans les groups de Lie”, J. Sci. Hiroshima Univ., 23:3 (1960), 311–324 | MR | Zbl

[11] M. M. Postnikov, Vvedenie v teoriyu Morsa, izd-vo «Nauka», Moskva, 1971 | MR

[12] H. Wang, “Discrete subgroups of solvable Lie groups, I”, Ann. Math., 64:1 (1956), 1–19 | DOI | MR | Zbl

[13] H. Wang, “On the deformations of lattice in a Lie group”, Amer. J. Math., 85:2 (1963), 189–212 | DOI | MR | Zbl

[14] A. Weil, “On discrete subgroups of Lie groups, I”, Ann. Math., 72:2 (1960), 369–384 | DOI | MR