J{\o}rgensen Number and Arithmeticity
Geometric Topology
2013-01-29 v1 Group Theory
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.
Keywords
Cite
@article{arxiv.0905.1318,
title = {J{\o}rgensen Number and Arithmeticity},
author = {Jason Callahan},
journal= {arXiv preprint arXiv:0905.1318},
year = {2013}
}
Comments
27 pages, 2 figures