Local topology in deformation spaces of hyperbolic 3-manifolds

Abstract

We prove that the deformation space AH(M) of marked hyperbolic 3-manifolds homotopy equivalent to a fixed compact 3-manifold M with incompressible boundary is locally connected at minimally parabolic points. Moreover, spaces of Kleinian surface groups are locally connected at quasiconformally rigid points. Similar results are obtained for deformation spaces of acylindrical 3-manifolds and Bers slices.

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• Train tracks and the Gromov boundary of the complex of curves
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• Skinning maps
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Cited by in corpus (4)

• Dynamics on the PSL(2,C)-character variety of a compression body
• Convergence and divergence of Kleinian surface groups
• The Double Limit Theorem and its Legacy
• Geometric limits of cyclic subgroups of SO_0(1, k+1) and SU(1, k+1)