Uniform growth of groups acting on Cartan–Hadamard spaces

Besson, Gérard, Courtois, Gilles, and Gallot, Sylvestre. "Uniform growth of groups acting on Cartan–Hadamard spaces." Journal of the European Mathematical Society 013.5 (2011): 1343-1371. <http://eudml.org/doc/277249>.

@article{Besson2011,
abstract = {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.},
author = {Besson, Gérard, Courtois, Gilles, Gallot, Sylvestre},
journal = {Journal of the European Mathematical Society},
keywords = {finitely generated groups; groups acting on Cartan-Hadamard spaces; Tits alternative; manifolds with pinched negative curvature; algebraic entropy; isometry groups; virtually nilpotent groups; groups of uniform growth; finitely generated groups; groups acting on Cartan-Hadamard spaces; Tits alternative; manifolds with pinched negative curvature; algebraic entropy; isometry groups; virtually nilpotent groups; groups of uniform growth},
language = {eng},
number = {5},
pages = {1343-1371},
publisher = {European Mathematical Society Publishing House},
title = {Uniform growth of groups acting on Cartan–Hadamard spaces},
url = {http://eudml.org/doc/277249},
volume = {013},
year = {2011},
}

TY - JOUR
AU - Besson, Gérard
AU - Courtois, Gilles
AU - Gallot, Sylvestre
TI - Uniform growth of groups acting on Cartan–Hadamard spaces
JO - Journal of the European Mathematical Society
PY - 2011
PB - European Mathematical Society Publishing House
VL - 013
IS - 5
SP - 1343
EP - 1371
AB - 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.
LA - eng
KW - finitely generated groups; groups acting on Cartan-Hadamard spaces; Tits alternative; manifolds with pinched negative curvature; algebraic entropy; isometry groups; virtually nilpotent groups; groups of uniform growth; finitely generated groups; groups acting on Cartan-Hadamard spaces; Tits alternative; manifolds with pinched negative curvature; algebraic entropy; isometry groups; virtually nilpotent groups; groups of uniform growth
UR - http://eudml.org/doc/277249
ER -