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This article is cited in 1 scientific paper (total in 1 paper)
Large hyperbolic lattices
F. Grunewalda, G. A. Noskovb a Mathematisches Institut der Heinrich-Heine-Universität, Düsseldorf, Germany
b Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science, Omsk, Russia
Abstract:
For a fundamental group of a compact orientable manifold, a condition is specified that is sufficient to guarantee the presence of a “virtual” epimorphism onto a free non-Abelian group. A consequence is deriving a strong Tits alternative. An arbitrary noncompact finitely generated discrete subgroup in $\mathrm{PO}(3,1)$ either is large or is virtually Abelian. An application is provided to the problem of uniform exponential growth for lattices in a 3-dimensional hyperbolic space and of growth of Betti numbers for lattices in a hyperbolic $n$-dimensional space, where $n$ is an odd number.
Keywords:
fundamental group, compact orientable manifold, discrete subgroup, hyperbolic lattice, uniform exponential growth problem.
Received: 03.02.2009
Citation:
F. Grunewald, G. A. Noskov, “Large hyperbolic lattices”, Algebra Logika, 48:2 (2009), 174–189; Algebra and Logic, 48:2 (2009), 99–107
Linking options:
https://www.mathnet.ru/eng/al395 https://www.mathnet.ru/eng/al/v48/i2/p174
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Abstract page: | 330 | Full-text PDF : | 86 | References: | 52 | First page: | 3 |
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