Drilling cores of hyperbolic 3-manifolds to prove tameness
| dc.creator | Choi, Suhyoung | |
| dc.date | 2004-10-18 | |
| dc.date.accessioned | 2026-07-07T05:13:21Z | |
| dc.date.available | 2026-07-07T05:13:21Z | |
| dc.description | We supply a proof of the fact that a hyperbolic 3-manifold $M$ with finitely generated fundamental group and with no parabolics is topologically tame. This proves the Marden's conjecture. Our approach is to form an exhaustion $M_i$ of $M$ and modify the boundary to make them 2-convex. We use the induced path-metric, which makes the submanifold $M_i$ $δ$-hyperbolic and with Margulis constants independent of $i$. By taking the convex hull in the cover of $M_i$ corresponding the core, we show that there exists an exiting sequence of surfaces $Σ_i$. We drill out the covers of $M_i$ by a core $C$ again to make it $δ$-hyperbolic. Then the boundary of the convex hull of $Σ_i$ is shown to meet the core. By the compactness argument of Souto, we show that infinitely many of $Σ_i$ are homotopic in $M - C^o$. | |
| dc.description | 50 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math/0410381 | |
| dc.identifier | http://arxiv.org/abs/math/0410381 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72913 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M50 | |
| dc.title | Drilling cores of hyperbolic 3-manifolds to prove tameness | |
| dc.type | text |