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 < 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 GΓ 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