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Sibirskii Matematicheskii Zhurnal, 2014, Volume 55, Number 5, Pages 989–1000 (Mi smj2585)  
This article is cited in 6 scientific papers (total in 6 papers)

On Jørgensen numbers and their analogs for groups of figure-eight orbifolds

A. Yu. Vesninab, A. V. Masleycd

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Omsk State Technical University, Omsk, Russia
c Chelyabinsk State University, Chelyabinsk, Russia
d Novosibirsk State University, Novosibirsk, Russia
Full-text PDF (336 kB) Citations (6)
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Abstract: The Jørgensen, Gehring–Martin–Tan, and Tan numbers are defined for every two-generated subgroup of the group $\mathrm{PSL}(2,\mathbb C)$. These numbers arise in necessary discreteness conditions for two-generated subgroups. The Jørgensen number equals 1 for the figure-eight knot group. We calculate the above numbers or give some two-sided bounds of them for this group and groups of hyperbolic orbifolds with singularities along the figure-eight knot.
Keywords: hyperbolic space, discrete group of transformations, knot, orbifold.
Received: 24.02.2014
English version:
Siberian Mathematical Journal, 2014, Volume 55, Issue 5, Pages 807–816
DOI: https://doi.org/10.1134/S0037446614050036
Bibliographic databases:
Document Type: Article
UDC: 514.132+512.817
Language: Russian
Citation: A. Yu. Vesnin, A. V. Masley, “On Jørgensen numbers and their analogs for groups of figure-eight orbifolds”, Sibirsk. Mat. Zh., 55:5 (2014), 989–1000; Siberian Math. J., 55:5 (2014), 807–816
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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