Deformation spaces of Kleinian surface groups are not locally connected

Magid, Aaron D¹

¹ Department of Mathematics, University of Maryland, 1301 Campus Drive, College Park MD 20742, USA

Geometry & topology, Tome 16 (2012) no. 3, pp. 1247-1320.

Résumé

For any closed surface $S$ of genus $g\ge 2$, we show that the deformation space $AH\left(S\times I\right)$ of marked hyperbolic $3$–manifolds homotopy equivalent to $S$ 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.

Détail

DOI : 10.2140/gt.2012.16.1247

Classification : 57M50, 30F40
Keywords: hyperbolic, Kleinian group, deformation, hyperbolic Dehn filling, drilling, locally connected

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