Deformation spaces of Kleinian surface groups are not locally connected
| Autor: | Aaron D. Magid |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2010 |
| Předmět: |
0209 industrial biotechnology
Pure mathematics 02 engineering and technology locally connected Space (mathematics) 01 natural sciences drilling 30F40 Mathematics - Geometric Topology hyperbolic 020901 industrial engineering & automation Genus (mathematics) FOS: Mathematics 0101 mathematics hyperbolic Dehn filling 57M50 30F40 Mathematics Conjecture Kleinian group Homotopy 010102 general mathematics deformation Torus Geometric Topology (math.GT) Surface (topology) Mathematics::Geometric Topology 57M50 Algebra Locally connected space Geometry and Topology |
| Zdroj: | Geom. Topol. 16, no. 3 (2012), 1247-1320 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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