Uniform growth of groups acting on Cartan–Hadamard spaces
Journal of the European Mathematical Society, Tome 13 (2011) no. 5, pp. 1343-1371
Cet article a éte moissonné depuis 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.
@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
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
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