A. Yu. Vesnin, A. V. Masley, “On Jørgensen numbers and their analogs for groups of figure-eight orbifolds”, Sibirsk. Mat. Zh., 2014, Volume 55, Number 5,Pages <nobr>989

This article is cited in 6 papers

On Jørgensen numbers and their analogs for groups of figure-eight orbifolds

A. Yu. Vesnin^ab, A. V. Masley^cd

^a Sobolev Institute of Mathematics, Novosibirsk, Russia
^b Omsk State Technical University, Omsk, Russia
^c Chelyabinsk State University, Chelyabinsk, Russia
^d Novosibirsk State University, Novosibirsk, Russia

Abstract: The Jørgensen, Gehring–Martin–Tan, and Tan numbers are defined for every two-generated subgroup of the group $\mathrm{PSL}(2,\mathbb C)$. These numbers arise in necessary discreteness conditions for two-generated subgroups. The Jørgensen number equals 1 for the figure-eight knot group. We calculate the above numbers or give some two-sided bounds of them for this group and groups of hyperbolic orbifolds with singularities along the figure-eight knot.

Keywords: hyperbolic space, discrete group of transformations, knot, orbifold.

UDC: 514.132+512.817

Received: 24.02.2014