Jørgensen Number and Arithmeticity

Details Jørgensen Number and Arithmeticity Jørgensen Number and Arithmeticity

2009-05-08

arxiv.org/abs/0905.1318v1

Mathematics

Geometric Topology

27 pages, 2 figures

Scientific paper

A J{\o}rgensen group is a non-elementary Kleinian group that can be generated by two elements for which equality holds in J{\o}rgensen's Inequality. This paper shows that the only torsion-free J{\o}rgensen group is the figure-eight knot group, identifies all non-cocompact arithmetic J{\o}rgensen groups, and establishes a characterization of cocompact arithmetic J{\o}rgensen groups. The paper also defines and computes the J{\o}rgensen number of several non-cocompact Kleinian groups including some two-bridge knot and link groups.

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