Volume 13, issue 5 (2009)

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Free groups in lattices

Lewis Bowen

Geometry & Topology 13 (2009) 3021–3054
Abstract

Let $G$ be any locally compact unimodular metrizable group. The main result of this paper, roughly stated, is that if $F is any finitely generated free group and $\Gamma any lattice, then up to a small perturbation and passing to a finite index subgroup, $F$ is a subgroup of $\Gamma$. If $G∕\Gamma$ is noncompact then we require additional hypotheses that include $G=SO\left(n,1\right)$.

Keywords
free group, surface group, Kleinian group, limit set
Mathematical Subject Classification 2000
Primary: 20E07
Secondary: 20F65, 20F67, 22D40, 20E05