Uniform growth of groups acting on Cartan–Hadamard spaces
Journal of the European Mathematical Society, Tome 13 (2011) no. 5, pp. 1343-1371
Voir la notice de l'article provenant de la source EMS Press
In this paper we investigate the growth of finitely generated groups. We recall the definition of the algebraic entropy of a group and show that if the group is acting as a discrete subgroup of the isometry group of a Cartan–Hadamard manifold with pinched negative curvature then a Tits alternative is true. More precisely the group is either virtually nilpotent or has a uniform growth bounded below by an explicit constant.
Gérard Besson; Gilles Courtois; Sylvestre Gallot. Uniform growth of groups acting on Cartan–Hadamard spaces. Journal of the European Mathematical Society, Tome 13 (2011) no. 5, pp. 1343-1371. doi: 10.4171/jems/283
@article{JEMS_2011_13_5_a4,
author = {G\'erard Besson and Gilles Courtois and Sylvestre Gallot},
title = {Uniform growth of groups acting on {Cartan{\textendash}Hadamard} spaces},
journal = {Journal of the European Mathematical Society},
pages = {1343--1371},
year = {2011},
volume = {13},
number = {5},
doi = {10.4171/jems/283},
url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/283/}
}
TY - JOUR AU - Gérard Besson AU - Gilles Courtois AU - Sylvestre Gallot TI - Uniform growth of groups acting on Cartan–Hadamard spaces JO - Journal of the European Mathematical Society PY - 2011 SP - 1343 EP - 1371 VL - 13 IS - 5 UR - http://geodesic.mathdoc.fr/articles/10.4171/jems/283/ DO - 10.4171/jems/283 ID - JEMS_2011_13_5_a4 ER -
%0 Journal Article %A Gérard Besson %A Gilles Courtois %A Sylvestre Gallot %T Uniform growth of groups acting on Cartan–Hadamard spaces %J Journal of the European Mathematical Society %D 2011 %P 1343-1371 %V 13 %N 5 %U http://geodesic.mathdoc.fr/articles/10.4171/jems/283/ %R 10.4171/jems/283 %F JEMS_2011_13_5_a4
Cité par Sources :