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(π1(N)), the space of marked hyperbolic 3-manifolds homotopy equivalent to N. We will give topological conditions on N sufficient to give ρ ∈ B¯ such that for every sufficiently small neighbourhood V of ρ, V ⋂ B is disconnected. This implies that B is not a manifold with boundary. © 2001 Applied Probability Trust.