Proceedings of the Japan Academy, Series A, Mathematical Sciences

Note on non-discrete complex hyperbolic triangle groups of type $(n,n,\infty;k)$

Shigeyasu Kamiya

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Abstract

A complex hyperbolic triangle group is a group generated by three complex involutions fixing complex lines in complex hyperbolic space. In a previous paper~[3] we discussed complex hyperbolic triangle groups of type $(n,n,\infty;k)$ and proved that for $n \geq 29$ these groups are not discrete. In this paper we show that if $n \geq 22$, then complex hyperbolic triangle groups of type $(n,n,\infty;k)$ are not discrete and give a new list of non-discrete groups of type $(n,n,\infty;k)$.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 89, Number 8 (2013), 100-102.

Dates
First available in Project Euclid: 17 October 2013

Permanent link to this document
https://projecteuclid.org/euclid.pja/1382016181

Digital Object Identifier
doi:10.3792/pjaa.89.100

Mathematical Reviews number (MathSciNet)
MR3127925

Zentralblatt MATH identifier
1294.22007

Subjects
Primary: 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx] 32Q45: Hyperbolic and Kobayashi hyperbolic manifolds 51M10: Hyperbolic and elliptic geometries (general) and generalizations

Keywords
Complex hyperbolic triangle group complex involution

Citation

Kamiya, Shigeyasu. Note on non-discrete complex hyperbolic triangle groups of type $(n,n,\infty;k)$. Proc. Japan Acad. Ser. A Math. Sci. 89 (2013), no. 8, 100--102. doi:10.3792/pjaa.89.100. https://projecteuclid.org/euclid.pja/1382016181


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References

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