Commensurability and locally free Kleinian groups

Details Commensurability and locally free Kleinian groups Commensurability and locally free Kleinian groups

1999-03-23

arxiv.org/abs/math/9903138v1

Mathematics

Geometric Topology

14 pages

Scientific paper

We show that there exist infinitely many commensurability classes of finite volume hyperbolic 3-manifolds whose fundamental group contains a subgroup which is locally free but not free. The main technical tool is the fact that a collection of hyperbolic 3-manifolds of bounded volume contains infinitely many commensurability classes. The result then by an application of Thurston's hyperbolization theorem for Haken 3-manifolds.

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