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Complex hyperbolic
geometry of the figure-eight knot
Martin Deraux and Elisha Falbel |
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Geometry & Topology 19 (2015) 237–293
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Abstract |
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We show that the figure-eight knot complement admits a uniformizable spherical structure, ie it occurs as the manifold at infinity of a complex hyperbolic orbifold. The uniformization is unique provided we require the peripheral subgroups to have unipotent holonomy. |
Keywords
spherical CR structures, geometric structures on
$3$–manifolds, complex hyperbolic geometry
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Mathematical Subject Classification 2010
Primary: 32V05, 57M50
Secondary: 22E40
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References |
Publication
Received: 27 March 2013
Revised: 11 February 2014
Accepted: 1 May 2014
Published: 27 February 2015
Proposed: Walter Neumann
Seconded: Benson Farb, Danny Calegari
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Authors |
| Martin Deraux | |
| Institut Fourier Université de Grenoble 1 BP 74 Saint Martin d’Hères, Cedex France |
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| Elisha Falbel | |
| Institut de Mathématiques Université Pierre et Marie Curie 4 place Jussieu F-75252 Paris France |
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