Mathematics – Geometric Topology
Scientific paper
2006-02-23
Mathematics
Geometric Topology
This is a revision of math.GT/0410381
Scientific paper
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 $\Sigma_i$. 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 $\Sigma_i$ is shown to meet the core. By the compactness argument of Souto, we show that infinitely many of $\Sigma_i$ are homotopic in $M - \core^o$. Our method should generalize to a more wider class of piecewise hyperbolic manifolds.
No associations
LandOfFree
The PL-methods for hyperbolic 3-manifolds to prove tameness does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The PL-methods for hyperbolic 3-manifolds to prove tameness, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The PL-methods for hyperbolic 3-manifolds to prove tameness will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-711678