  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.
