Elder siblings and the taming of hyperbolic 3-manifolds

  title={Elder siblings and the taming of hyperbolic 3-manifolds},
  author={Michael H. Freedman and Curtis T Mcmullen},
A 3-manifold is tame if it is homeomorphic to the interior of a compact manifold with boundary. Marden’s conjecture asserts that any hyperbolic 3-manifold M = H/Γ with π1(M) finitely-generated is tame. This paper presents a criterion for tameness. We show that wildness of M is detected by large-scale knotting of orbits of Γ. The elder sibling property prevents knotting and implies tameness by a Morse theory argument. We also show the elder sibling property holds for all convex cocompact groups… CONTINUE READING

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