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Algebra i logika, 2009, Volume 48, Number 2, Pages 174–189 (Mi al395)  

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
Full-text PDF (217 kB) Citations (1)
References:
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
English version:
Algebra and Logic, 2009, Volume 48, Issue 2, Pages 99–107
DOI: https://doi.org/10.1007/s10469-009-9049-x
Bibliographic databases:
UDC: 512.5
Language: Russian
Citation: F. Grunewald, G. A. Noskov, “Large hyperbolic lattices”, Algebra Logika, 48:2 (2009), 174–189; Algebra and Logic, 48:2 (2009), 99–107
Citation in format AMSBIB
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\paper Large hyperbolic lattices
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  • https://www.mathnet.ru/eng/al/v48/i2/p174
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и логика Algebra and Logic
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    Abstract page:330
    Full-text PDF :86
    References:52
    First page:3
     
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