Uniform growth of groups acting on Cartan–Hadamard spaces

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 i...

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Veröffentlicht in:Journal of the European Mathematical Society : JEMS 2011-01, Vol.13 (5), p.1343-1371
Hauptverfasser: Besson, Gérard, Courtois, Gilles, Gallot, Sylvestre
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Sprache:eng
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Zusammenfassung: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.
ISSN:1435-9855
1435-9863
DOI:10.4171/JEMS/283