Abstract:
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.
\Bibitem{Gor73}
\by V.~V.~Gorbatsevich
\paper Lattices in solvable Lie groups and deformations of homogeneous spaces
\jour Math. USSR-Sb.
\yr 1973
\vol 20
\issue 2
\pages 249--266
\mathnet{http://mi.mathnet.ru/eng/sm3114}
\crossref{https://doi.org/10.1070/SM1973v020n02ABEH001873}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=352329}
\zmath{https://zbmath.org/?q=an:0286.22008}
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https://www.mathnet.ru/eng/sm3114
https://doi.org/10.1070/SM1973v020n02ABEH001873
https://www.mathnet.ru/eng/sm/v133/i2/p234
This publication is cited in the following 10 articles:
Rachel Nicks, “A Classification of the Symmetries of Uniform Discrete Defective Crystals”, J Elast, 2014
Rachel Nicks, Gareth Parry, “Group Elastic Symmetries Common to Continuum and Discrete Defective Crystals”, J Elast, 2013
Rachel Nicks, Gareth P Parry, “On symmetries of crystals with defects related to a class of solvable groups (S1)”, Mathematics and Mechanics of Solids, 17:6 (2012), 631
Wim Malfait, “Nielsen’s theorem for model aspherical manifolds”, manuscripta math, 90:1 (1996), 63
Dave Witte, “Superrigidity of lattices in solvable Lie groups”, Invent Math, 122:1 (1995), 147
Paul Igodt, Wim Malfait, “Extensions realising a faithful abstract kernel and their automorphisms”, manuscripta math, 84:1 (1994), 135
V. V. Gorbatsevich, “On the number of Lie groups containing uniform lattices isomorphic to a given group”, Math. USSR-Izv., 30:3 (1988), 487–501
Gorbatsevich V., “Lie-Groups with Lattices and their Properties”, 287, no. 1, 1986, 33–37
V. V. Gorbatsevich, “On Lie groups, transitive on compact solvmanifolds”, Math. USSR-Izv., 11:2 (1977), 271–292
V. V. Gorbatsevich, “On aspherical homogeneous spaces”, Math. USSR-Sb., 29:2 (1976), 223–238
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