Groups generated by two elliptic elements in PU(2,1)

Details Groups generated by two elliptic elements in PU(2,1) Groups generated by two elliptic elements in PU(2,1)

2010-03-14

arxiv.org/abs/1003.2789v1

Mathematics

Complex Variables

9 pages

Scientific paper

Let $f$ and $g$ be two elliptic elements in $\mathbf{PU}(2,1)$ of order $m$
and $n$ respectively, where $m\geq n>2$. We prove that if the distance
$\delta(f,g)$ between the complex lines or points fixed by $f$ and $g$ is large
than a certain number, then the group $< f, g >$ is discrete nonelementary and
isomorphic to the free product $\mathbf{Z}_{m}*\mathbf{Z}_{n}$.

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