Deformation spaces of Kleinian surface groups are not locally connected

Aaron D. Magid

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arXiv · 1003.4541

Deformation spaces of Kleinian surface groups are not locally connected

Aaron D. Magid

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Abstract

For any closed surface $S$ of genus $g \geq 2$, we show that the deformation space of marked hyperbolic 3-manifolds homotopy equivalent to $S$, $AH(S \times I)$, is not locally connected. This proves a conjecture of Bromberg who recently proved that the space of Kleinian punctured torus groups is not locally connected. Playing an essential role in our proof is a new version of the filling theorem that is based on the theory of cone-manifold deformations developed by Hodgson, Kerckhoff, and Bromberg.

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Aaron D. Magid. 2010-03-23. Deformation spaces of Kleinian surface groups are not locally connected. https://arxiv.org/abs/1003.4541

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