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Margulis Lemma, entropy and free products

Filippo Cerocchi — 2014

Annales de l’institut Fourier

We prove a Margulis’ Lemma 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.

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