Geometry & Topology

Free groups in lattices

Lewis Bowen

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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).

Article information

Source
Geom. Topol., Volume 13, Number 5 (2009), 3021-3054.

Dates
Received: 27 May 2007
Revised: 26 August 2009
Accepted: 17 August 2009
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513800326

Digital Object Identifier
doi:10.2140/gt.2009.13.3021

Mathematical Reviews number (MathSciNet)
MR2546620

Zentralblatt MATH identifier
1244.22003

Subjects
Primary: 20E07: Subgroup theorems; subgroup growth
Secondary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 20F67: Hyperbolic groups and nonpositively curved groups 22D40: Ergodic theory on groups [See also 28Dxx] 20E05: Free nonabelian groups

Keywords
free group surface group Kleinian group limit set

Citation

Bowen, Lewis. Free groups in lattices. Geom. Topol. 13 (2009), no. 5, 3021--3054. doi:10.2140/gt.2009.13.3021. https://projecteuclid.org/euclid.gt/1513800326


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