= Jørgensen's inequality
{c}
{title2=$|\operatorname{tr}^2A-4|+|\operatorname{tr}[A,B]-2|\ge1$}
{wiki}
= Jorgensen inequality
{c}
{synonym}
For a non-elementary <discrete subgroup> generated by $A,B\in\operatorname{SL}(2,\mathbb C)$, the displayed inequality is a necessary trace constraint. Failure of it proves nondiscreteness when non-elementarity has independently been checked. It is not a sufficient condition for discreteness and must not be applied to an elementary pair without its hypothesis.
Back to article page
