# Uniform growth of groups acting on Cartan–Hadamard spaces

Gérard Besson; Gilles Courtois; Sylvestre Gallot

Journal of the European Mathematical Society (2011)

- Volume: 013, Issue: 5, page 1343-1371
- ISSN: 1435-9855

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topBesson, 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 -

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