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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.

Self-Bumping of Deformation Spaces of Hyperbolic 3-Manifolds