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arxiv: math/9903138 · v1 · submitted 1999-03-23 · 🧮 math.GT

Commensurability and locally free Kleinian groups

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keywords commensurabilityfreemanifoldsclassescontainshyperbolicinfinitelylocally
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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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