| Título: | Elder Siblings and the Taming of Hyperbolic 3-Manifolds |
| Autores: |
Freedman, Michael H. McMullen, Curtis T. |
| Fecha: |
2009-12-21 1998 2009-12-21 |
| Publicador: | Academia Scientiarum Fennica |
| Fuente: |
Ver documento |
| Tipo: | Journal Article |
| Tema: | |
| Descripción: |
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 \(\mathbb{M} = \mathbb{H}^3/\Gamma\) 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. Mathematics |
| Idioma: | Inglés |
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