Osaka Journal of Mathematics

Conjugacy class and discreteness in $\mathit{SL}(2, \mathbb{C})$

Shihai Yang and Tiehong Zhao

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In this note we establish a new discreteness criterion for a non-elementary group $G$ in $\mathit{SL}(2, \mathbb{C})$. Namely, $G$ is discrete if all the two-generator subgroups are discrete, where one generator is a non-trivial element $f$ in $G$, and the other is in the conjugacy class of $f$.

Article information

Osaka J. Math., Volume 53, Number 4 (2016), 1047-1053.

First available in Project Euclid: 4 October 2016

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Zentralblatt MATH identifier

Primary: 30C62: Quasiconformal mappings in the plane 30F40: Kleinian groups [See also 20H10] 20H10: Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx]


Yang, Shihai; Zhao, Tiehong. Conjugacy class and discreteness in $\mathit{SL}(2, \mathbb{C})$. Osaka J. Math. 53 (2016), no. 4, 1047--1053.

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