J{\o}rgensen Number and Arithmeticity

Jason Callahan

doi:10.1090/s1088-4173-09-00196-9

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arXiv · 0905.1318

J{\o}rgensen Number and Arithmeticity

Jason Callahan

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Abstract

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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Jason Callahan. 2009-05-08. J{\o}rgensen Number and Arithmeticity. https://doi.org/10.1090/s1088-4173-09-00196-9

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