Sufficient discreteness conditions for $2$-generator subgroups in $\mathrm{PSL}(2,\mathbb C)$

A. V. Masley

Novosibirsk State University, Novosibirsk, Russia

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.

UDC: 514.132+512.817

Received: 28.03.2013

 English version: Siberian Mathematical Journal, 2013, 54:5, 857–870

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