Remark on discrete subgroups
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- by Joseph A. Wolf PDF
- Proc. Amer. Math. Soc. 29 (1971), 423-425 Request permission
Abstract:
One wants to know the extent to which a locally compact group G is determined by the isomorphism class of a discrete uniform subgroup $\Gamma$. Among other things, we show that if G has only finitely many components and K is a maximal compact subgroup then $\Gamma$ determines the dimension of the space $G/K$. We then specialize our results to the case where $G/K$ is a riemannian symmetric space.References
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G. D. Mostow, Results announced at the International Congress of Mathematicians, Nice, 1970 (to appear).
- Atle Selberg, On discontinuous groups in higher-dimensional symmetric spaces, Contributions to function theory (Internat. Colloq. Function Theory, Bombay, 1960) Tata Institute of Fundamental Research, Bombay, 1960, pp. 147–164. MR 0130324
- E. Spanier, Duality in topological manifolds, Colloque de Topologie (Brussels, 1964) Librairie Universitaire, Louvain, 1966, pp. 91–111. MR 0220297
- Joseph A. Wolf, Discrete groups, symmetric spaces, and global holonomy, Amer. J. Math. 84 (1962), 527–542. MR 148013, DOI 10.2307/2372860
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 423-425
- MSC: Primary 22.20
- DOI: https://doi.org/10.1090/S0002-9939-1971-0279237-2
- MathSciNet review: 0279237