Freedman, Michael H.McMullen, Curtis2009-12-211998Freedman, Michael H. and Curtis T. McMullen. 1998. Elder siblings and the taming of hyperbolic 3-manifolds. Annales Academiae Scientiarum Fennicae 23: 415–428. Revised 2003.1239-629Xhttp://nrs.harvard.edu/urn-3:HUL.InstRepos:3446000A 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 \(\mathbb{M} = \mathbb{H}^3/\Gamma\) with \(\pi_1(M)\) finitely-generated is tame. This paper presents a criterion for tameness. We show that wildness of \(\mathbb{M}\) is detected by large-scale knotting of orbits of \(\Gamma\). 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 and a strict form of it characterizes such groups.en-USJournal Article2009-12-21