The PL-methods for hyperbolic 3-manifolds to prove tameness
| dc.creator | Choi, Suhyoung | |
| dc.date | 2006-02-23 | |
| dc.date.accessioned | 2026-07-07T07:03:42Z | |
| dc.date.available | 2026-07-07T07:03:42Z | |
| dc.description | Using PL-methods, we prove the Marden's conjecture that a hyperbolic 3-manifold $M$ with finitely generated fundamental group and with no parabolics are topologically tame. 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 $M_i$ negatively curved and with Margulis constant independent of $i$. By taking the convex hull in the cover of $M_i$ corresponding to the core, we show that there exists an exiting sequence of surfaces $Σ_i$. Some of the ideas follow those of Agol. We drill out the covers of $M_i$ by a core $\core$ again to make it negatively curved. 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 $M - \core^o$. Our method should generalize to a more wider class of piecewise hyperbolic manifolds. | |
| dc.description | This is a revision of math.GT/0410381 | |
| dc.identifier | https://arxiv.org/abs/math/0602520 | |
| dc.identifier | http://arxiv.org/abs/math/0602520 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/109076 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M50 | |
| dc.title | The PL-methods for hyperbolic 3-manifolds to prove tameness | |
| dc.type | text |