Quasi-isometrically embedded free sub-semigroups
Geometry & topology, Tome 12 (2008) no. 1, pp. 461-473.

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

If G is either a connected Lie group, or a finitely generated solvable group with exponential growth, we show that G contains a quasi-isometrically embedded free sub-semigroup on 2 generators.

DOI : 10.2140/gt.2008.12.461
Keywords: Tits alternative, ping-pong Lemma, just non-virtually nilpotent groups

de Cornulier, Yves 1 ; Tessera, Romain 2

1 IRMAR, Campus de Beaulieu, 35042 Rennes Cedex, France
2 Department of Mathematics, Stevenson Center, Vanderbilt University, Nashville TN 37240, USA
@article{GT_2008_12_1_a10,
     author = {de Cornulier, Yves and Tessera, Romain},
     title = {Quasi-isometrically embedded free sub-semigroups},
     journal = {Geometry & topology},
     pages = {461--473},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2008},
     doi = {10.2140/gt.2008.12.461},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/gt.2008.12.461/}
}
TY  - JOUR
AU  - de Cornulier, Yves
AU  - Tessera, Romain
TI  - Quasi-isometrically embedded free sub-semigroups
JO  - Geometry & topology
PY  - 2008
SP  - 461
EP  - 473
VL  - 12
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2140/gt.2008.12.461/
DO  - 10.2140/gt.2008.12.461
ID  - GT_2008_12_1_a10
ER  - 
%0 Journal Article
%A de Cornulier, Yves
%A Tessera, Romain
%T Quasi-isometrically embedded free sub-semigroups
%J Geometry & topology
%D 2008
%P 461-473
%V 12
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2140/gt.2008.12.461/
%R 10.2140/gt.2008.12.461
%F GT_2008_12_1_a10
de Cornulier, Yves; Tessera, Romain. Quasi-isometrically embedded free sub-semigroups. Geometry & topology, Tome 12 (2008) no. 1, pp. 461-473. doi : 10.2140/gt.2008.12.461. http://geodesic.mathdoc.fr/articles/10.2140/gt.2008.12.461/

[1] S I Adian, Random walks on free periodic groups, Math. USSR Izvestiya 21 (1983) 425

[2] I Benjamini, O Schramm, Every graph with a positive Cheeger constant contains a tree with a positive Cheeger constant, Geom. Funct. Anal. 7 (1997) 403

[3] N Bourbaki, Groupes et algèbres de Lie. Chapitres 4, 5 et 6, Éléments de mathématique, Masson (1981) 290

[4] J Bourgain, The metrical interpretation of superreflexivity in Banach spaces, Israel J. Math. 56 (1986) 222

[5] E Breuillard, On uniform exponential growth for solvable groups, Pure and Applied Math Quarterly 3(4) (2007) 949

[6] B Farb, The extrinsic geometry of subgroups and the generalized word problem, Proc. London Math. Soc. $(3)$ 68 (1994) 577

[7] M Gromov, Asymptotic invariants of infinite groups, from: "Geometric group theory, Vol. 2 (Sussex, 1991)", London Math. Soc. Lecture Note Ser. 182, Cambridge Univ. Press (1993) 1

[8] J R J Groves, Soluble groups with every proper quotient polycyclic, Illinois J. Math. 22 (1978) 90

[9] A Y Ol’Shanskiĭ, On the distortion of subgroups of finitely presented groups, Mat. Sb. 188 (1997) 51

[10] D Osin, Subgroup distortions in nilpotent groups, Comm. Algebra 29 (2001) 5439

[11] D Osin, Small cancellations over relatively hyperbolic groups and embedding theorems

[12] J M Rosenblatt, Invariant measures and growth conditions, Trans. Amer. Math. Soc. 193 (1974) 33

[13] R Tessera, Asymptotic isoperimetry on groups and uniform embeddings into Banach spaces

[14] R Tessera, Large-scale Sobolev inequalities on metric measure spaces

[15] J Tits, Free subgroups in linear groups, J. Algebra 20 (1972) 250

Cité par Sources :