Abstract
Continuing the study of quasicompact homogeneous spaces, we prove some previouslyannounced assertions and present some strengthenings for them. The new results of the article mainly concern the description of quasicompact homogeneous manifolds up to a finite covering.
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References
Gorbatsevich V. V. and Onishchik A. L., “Lie transformation groups,” in: Lie Groups and Lie Algebras I. Foundations of Lie Theory. Lie Transformation Groups., Encycl. Math. Sci., 20, 95–229 (1993).
Onishchik A. L., Topology of Transitive Transformation Groups, Johann Ambrosius Barth, Leipzig, Berlin, and Heidelberg (1994).
Gorbatsevich V. V., “On some classes of homogeneous spaces close to compact,” Soviet Math., Dokl., 38, No. 3, 592–596 (1989).
Gorbatsevich V. V., “Plesiocompact homogeneous spaces,” Siberian Math. J., 30, No. 2, 217–226 (1989).
Gorbatsevich V. V., “On the properties of plesio-uniform subgroups in Lie groups,” Math. Notes, 69, No. 3, 306–312 (2001).
Gorbatsevich V. V., “Compact homogeneous spaces and their generalizations,” J. Math. Sci., New York, 153, No. 6, 763–798 (2008).
Gorbatsevich V. V., “The structure of homogeneous spaces with a finite invariant metric,” Soviet Math. (Izv. VUZ. Mat.), 35, No. 7, 61–64 (1991).
Raghunathan M. S., Discrete Subgroups of Lie Groups, Springer-Verlag, Berlin, Heidelberg, and New York (1972).
Mostow G. D., “Homogeneous spaces with finite invariant measure,” Ann. Math., 75, No. I, 17–37 (1962).
Wang S. R., “Homogeneous spaces with finite invariant measure,” Amer. J. Math., 98, No. 2, 311–324 (1976).
Auslander L., Hahn F., and Green L., Flows on Homogeneous Spaces, Princeton University Press, Princeton, NJ (1963).
Gorbatsevich V. V., “Three-dimensional homogeneous spaces,” Siberian Math. J., 18, No. 2, 200–210 (1977).
Gorbatsevich V. V., “Compact homogeneous manifolds of dimension at most 7 up to a finite covering,” Izv.: Math., 76, No. 4, 669–680 (2012).
Mostow G. D., “On the topology of homogeneous spaces of finite measure,” Sympos. Math., 16, 375–398 (1975).
Gorbacevic V. V., “Compact aspherical homogeneous spaces up to a finite covering,” Ann. Global. Anal. Geom., 1, No. 3, 103–118 (1983).
Zieschang H., Vogt E., and Coldewey H.-D., Surfaces and Planar Discontinuous Groups, Springer-Verlag, Berlin, Heidelberg, and New York (1980). pp. 243–246
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Original Russian Text Copyright © 2013 Gorbatsevich V.V.
The author was supported by the Russian Foundation for Basic Research (Grant 11-01-00465a).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 2, pp. 303–319, March–April, 2013.
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Gorbatsevich, V.V. On quasicompact homogeneous spaces. Sib Math J 54, 231–242 (2013). https://doi.org/10.1134/S0037446613020079
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DOI: https://doi.org/10.1134/S0037446613020079