Lemme de Margulis, entropie et produits libres

I shall show how we can obtain a Margulis' Lemma ê  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. I shall present examples and counterexamples showing the optimality of our assumption and two applications of this result: a finiteness theorem and a volume estimate without curvature assumptions for reducible manifolds