Jørgensen数与算术性
Jørgensen Number and Arithmeticity
摘要：
约根森群（英语：Jørgensen group）是一个非初等的克莱因群，它可以由两个元素生成，并且在约根森不等式中等式成立。本文证明了唯一无挠的Jørgensen群是8字形纽结群，并给出了所有非余紧算术Jørgensen群的定义，建立了余紧算术Jørgensen群的一个刻划.本文还定义并计算了几个非余紧克莱因群（包括一些二桥纽结群和链环群）的Jørgensen数。
英文摘要：
A Jørgensen group is a non-elementary Kleinian group that can be generated by two elements for which equality holds in Jørgensen's Inequality. This paper shows that the only torsion-free Jørgensen group is the figure-eight knot group, identifies all non-cocompact arithmetic Jørgensen groups, and establishes a characterization of cocompact arithmetic Jørgensen groups. The paper also defines and computes the Jørgensen number of several non-cocompact Kleinian groups including some two-bridge knot and link groups.
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