Geodesic
Free groups in lattices
Bowen, Lewis1
1 Department of Mathematics, University of Hawaii, Honolulu, HI 96822, USA
Geometry & topology, Tome 13 (2009) no. 5, pp. 3021-3054.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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).

DOI : 10.2140/gt.2009.13.3021
Keywords: free group, surface group, Kleinian group, limit set

Bowen, Lewis 1

1 Department of Mathematics, University of Hawaii, Honolulu, HI 96822, USA 
@article{GT_2009_13_5_a9,
     author = {Bowen, Lewis},
     title = {Free groups in lattices},
     journal = {Geometry & topology},
     pages = {3021--3054},
     publisher = {mathdoc},
     volume = {13},
     number = {5},
     year = {2009},
     doi = {10.2140/gt.2009.13.3021},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/gt.2009.13.3021/}
}
TY  - JOUR
AU  - Bowen, Lewis
TI  - Free groups in lattices
JO  - Geometry & topology
PY  - 2009
SP  - 3021
EP  - 3054
VL  - 13
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2140/gt.2009.13.3021/
DO  - 10.2140/gt.2009.13.3021
ID  - GT_2009_13_5_a9
ER  - 
%0 Journal Article
%A Bowen, Lewis
%T Free groups in lattices
%J Geometry & topology
%D 2009
%P 3021-3054
%V 13
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2140/gt.2009.13.3021/
%R 10.2140/gt.2009.13.3021
%F GT_2009_13_5_a9
Bowen, Lewis. Free groups in lattices. Geometry & topology, Tome 13 (2009) no. 5, pp. 3021-3054. doi : 10.2140/gt.2009.13.3021. http://geodesic.mathdoc.fr/articles/10.2140/gt.2009.13.3021/

[1] L Bowen, Periodicity and circle packings of the hyperbolic plane, Geom. Dedicata 102 (2003) 213

[2] L Bowen, C Holton, C Radin, L Sadun, Uniqueness and symmetry in problems of optimally dense packings, Math. Phys. Electron. J. 11 (2005)

[3] M R Bridson, A Haefliger, Metric spaces of non-positive curvature, Grund. der Math. Wissenschaften 319, Springer (1999)

[4] M Coornaert, Mesures de Patterson–Sullivan sur le bord d'un espace hyperbolique au sens de Gromov, Pacific J. Math. 159 (1993) 241

[5] M Coornaert, T Delzant, A Papadopoulos, Géométrie et théorie des groupes. Les groupes hyperboliques de Gromov, Lecture Notes in Math. 1441, Springer (1990)

[6] A Dranishnikov, V Schroeder, Aperiodic colorings and tilings of Coxeter groups, Groups Geom. Dyn. 1 (2007) 311

[7] V A Efremovič, The proximity geometry of Riemannian manifolds, Uspehi Matem. Nauk (N.S.) 8 (1953) 189

[8] C Goodman-Strauss, A strongly aperiodic set of tiles in the hyperbolic plane, Invent. Math. 159 (2005) 119

[9] M Gromov, Hyperbolic groups, from: "Essays in group theory", Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75

[10] M Lackenby, Surface subgroups of Kleinian groups with torsion, to appear in Invent. Math.

[11] M Lackenby, D D Long, A W Reid, LERF and the Lubotzky–Sarnak conjecture, Geom. Topol. 12 (2008) 2047

[12] G A Margulis, S Mozes, Aperiodic tilings of the hyperbolic plane by convex polygons, Israel J. Math. 107 (1998) 319

[13] J D Masters, Kleinian groups with ubiquitous surface subgroups, Groups Geom. Dyn. 2 (2008) 263

[14] C T Mcmullen, Hausdorff dimension and conformal dynamics. I. Strong convergence of Kleinian groups, J. Differential Geom. 51 (1999) 471

[15] J Milnor, A note on curvature and fundamental group, J. Differential Geometry 2 (1968) 1

[16] R Penrose, Pentaplexity: a class of nonperiodic tilings of the plane, Eureka 39 (1978) 16

[17] A S Švarc, A volume invariant of coverings, Dokl. Akad. Nauk SSSR $($N.S.$)$ 105 (1955) 32

[18] W A Veech, Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards, Invent. Math. 97 (1989) 553

Cité par Sources :