Margulis Lemma, entropy and free products
Annales de l'Institut Fourier, Volume 64 (2014) no. 3, pp. 1011-1030.

We prove a Margulis’ Lemma à la Besson-Courtois-Gallot, for manifolds whose fundamental group is a nontrivial free product A*B, without 2-torsion. Moreover, if A*B is torsion-free we give a lower bound for the homotopy systole in terms of upper bounds on the diameter and the volume-entropy. We also provide examples and counterexamples showing the optimality of our assumption. Finally we give two applications of this result: a finiteness theorem and a volume estimate for reducible manifolds.

Nous présentons une preuve d’un Lemme de Margulis à la Besson-Courtois-Gallot pour des variétés dont le groupe fondamental est un produit libre A*B non trivial et sans élément de torsion d’ordre 2. De plus, quand A*B est sans torsion nous donnons une minoration de la systole (homotopique) en fonction des bornes supérieurs sur le diamètre et sur l’entropie volumique. Nous allons fournir des exemples et des contre-exemples afin de montrer l’optimalité de nos hypothèses. Finalement, nous présentons deux applications de ce résultat  : un théorème de précompacité et finitude et une estimation volumique pour variétés décomposables.

DOI: 10.5802/aif.2872
Classification: 53C23, 53B21, 20E06, 20F65
Keywords: Entropy, growth of groups, free products, systole
Mot clés : entropie, croissance des groupes, produits libres, systole
Cerocchi, Filippo 1

1 Università di Roma “Sapienza” Dipartimento di Matematica “G. Castelnuovo” Piazzale Aldo Moro 5 00185 Roma (Italy) & Université Grenoble 1 Institut Fourier 100 rue des maths BP 74 38402 St. Martin d’Hères (France)
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Cerocchi, Filippo. Margulis Lemma, entropy and free products. Annales de l'Institut Fourier, Volume 64 (2014) no. 3, pp. 1011-1030. doi : 10.5802/aif.2872. https://aif.centre-mersenne.org/articles/10.5802/aif.2872/

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