We provide an infinite family of pared manifolds whose relative deformation spaces of hyperbolic structures on these manifolds are not locally connected. This is a natural extension of the recent result of Bromberg that shows the space of Kleinian punctured torus groups is not locally connected.
Hyperbolic Structures on 3-manifolds, I: Deformation of acylindrical manifolds
6j-symbols, hyperbolic structures and the Volume Conjecture
On the potential functions for the hyperbolic structures of a knot complement
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