A Lower Bound for the Exponent of Convergence of Normal Subgroups of Kleinian Groups

Details A Lower Bound for the Exponent of Convergence of Normal Subgroups of Kleinian Groups A Lower Bound for the Exponent of Convergence of Normal Subgroups of Kleinian Groups

2012-03-14

arxiv.org/abs/1203.3022v1

Mathematics

Complex Variables

Scientific paper

In this note we give a short new proof that for each non-elementary Kleinian group $\Gamma$, the exponent of convergence of an arbitrary non-trivial normal subgroup is bounded below by half of the exponent of convergence of $\Gamma$, and that strict inequality holds if $\Gamma$ is of divergence type. Our proof uses the existence of a certain uniformly finite-to-one map from a factor of $\Gamma$ to the normal subgroup.

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