Free groups in lattices

Bowen, Lewis

doi:10.2140/gt.2009.13.3021

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Free groups in lattices

Lewis Bowen

Geometry & Topology 13 (2009) 3021–3054

DOI: 10.2140/gt.2009.13.3021

Abstract

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

Keywords

free group, surface group, Kleinian group, limit set

Mathematical Subject Classification 2000

Primary: 20E07

Secondary: 20F65, 20F67, 22D40, 20E05

References

Publication

Received: 27 May 2007

Revised: 26 August 2009

Accepted: 17 August 2009

Published: 26 September 2009

Proposed: Martin Bridson

Seconded: Benson Farb, Jean-Pierre Otal

Authors

Lewis Bowen
Department of Mathematics University of Hawaii Honolulu, HI 96822 USA

Volume 13, issue 5 (2009)