Proceedings of the Japan Academy, Series A, Mathematical Sciences

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

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 our previous papers~[4,5,6,7,8] we discussed complex hyperbolic triangle groups. In particular, in~[5,8] we considered complex hyperbolic triangle groups of type $(n,n,\infty;k)$ and proved that for $n \geq 22$ these groups are not discrete. In this paper we show that if $n \geq 14$, 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 93, Number 7 (2017), 67-71.

Dates
First available in Project Euclid: 25 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.pja/1500969801

Digital Object Identifier
doi:10.3792/pjaa.93.67

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 $(n,n,\infty;k)$ II. Proc. Japan Acad. Ser. A Math. Sci. 93 (2017), no. 7, 67--71. doi:10.3792/pjaa.93.67. https://projecteuclid.org/euclid.pja/1500969801


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