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Sibirskii Matematicheskii Zhurnal, 2013, Volume 54, Number 5, Pages 1069–1086 (Mi smj2478)  
Sufficient discreteness conditions for $2$-generator subgroups in $\mathrm{PSL}(2,\mathbb C)$

A. V. Masley

Novosibirsk State University, Novosibirsk, Russia
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Abstract: Every element in $\mathrm{PSL}(2,\mathbb C)$ is elliptic, parabolic, or loxodromic. For the groups generated by two elliptic elements, sufficient discreteness conditions were obtained by Gehring, Maclachlan, Martin, and Rasskazov. In this article we establish sufficient discreteness conditions for the groups generated by two loxodromic elements and the groups generated by a loxodromic element and an elliptic element.
Keywords: Kleinian group, discrete group, hyperbolic geometry.
Received: 28.03.2013
English version:
Siberian Mathematical Journal, 2013, Volume 54, Issue 5, Pages 857–870
DOI: https://doi.org/10.1134/S0037446613050108
Bibliographic databases:
Document Type: Article
UDC: 514.132+512.817
Language: Russian
Citation: A. V. Masley, “Sufficient discreteness conditions for $2$-generator subgroups in $\mathrm{PSL}(2,\mathbb C)$”, Sibirsk. Mat. Zh., 54:5 (2013), 1069–1086; Siberian Math. J., 54:5 (2013), 857–870
Citation in format AMSBIB
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