Proceedings of the Japan Academy, Series A, Mathematical Sciences

A discrete criterion in $\mathit{PU}(2,1)$ by use of elliptic elements

Ainong Fang and Shihai Yang

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In this paper we show a $2$-dimensional subgroup in $\mathit{PU}(2,1)$ which contains elliptics is discrete if and only if all its subgroups generated by two elliptics are discrete. This generalize the well-known discreteness criterion first established by T. Jørgensen.

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Proc. Japan Acad. Ser. A Math. Sci., Volume 82, Number 3 (2006), 46-48.

First available in Project Euclid: 4 April 2006

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Primary: 30F40: Kleinian groups [See also 20H10] 30C60 20H10: Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx]

Discrete groups complex hyperbolic space elliptic elements


Yang, Shihai; Fang, Ainong. A discrete criterion in $\mathit{PU}(2,1)$ by use of elliptic elements. Proc. Japan Acad. Ser. A Math. Sci. 82 (2006), no. 3, 46--48. doi:10.3792/pjaa.82.46.

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