Self-bumping of deformation spaces of hyperbolic 3-manifolds

Abstract

Let $N$ be a hyperbolic 3-manifold and $B$ a component of the interior of $AH(\pi_1(N))$, the space of marked hyperbolic 3-manifolds homotopy equivalent to $N$. We will give topological conditions on $N$ sufficient to give $\rho \in \bar{B}$ such that for every small neighborhood $V$ of $\rho$, $V \cap B$ is disconnected. This implies that $\bar{B}$ is not manifold with boundary.