# Free versus locally free Kleinian groups.

• Juan Souto, Rennes
• Wednesday 30 April 2014, 16:00-17:00
• MR13.

It is well-known that a finitely generated torsion free Kleinian group without higher rank abelian subgroups and whose limit set is a Cantor set is isomorphic to a free group. What might be less well-known is that this fails for infinitely generated groups. Indeed one can prove that for each \epsilon>0 there is a torsion free non-elementary Kleinian group whose limit set is a Cantor set of Hausdorff dimension at most 1+\epsilon and which is not free. On the other hand, we prove that any torsion-free Kleinian group whose limit set has Hausdorff dimension less than 1 is indeed free. This is join work with Pekka Pankka.

This talk is part of the Differential Geometry and Topology Seminar series.