Margulis Lemma, entropy and free products

Details Margulis Lemma, entropy and free products Margulis Lemma, entropy and free products

2012-04-07

arxiv.org/abs/1204.1619v1

Mathematics

Differential Geometry

Scientific paper

We prove a Margulis' Lemma \`a 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.

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