Uniform growth of groups acting on Cartan�Hadamard spaces

• Autores: Gérard Besson, Gilles Courtois, Sylvestre Gallot
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 13, Nº 5, 2011, págs. 1343-1371
• Idioma: inglés
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• Resumen

  • 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.