Complex hyperbolic geometry of the figure-eight knot

Deraux, Martin¹ ; Falbel, Elisha²

¹ Institut Fourier, Université de Grenoble 1, BP 74, Saint Martin d’Hères, Cedex, France
² Institut de Mathématiques, Université Pierre et Marie Curie, 4 place Jussieu, F-75252 Paris, France

Geometry & topology, Tome 19 (2015) no. 1, pp. 237-293.

Résumé

We show that the figure-eight knot complement admits a uniformizable spherical $CR$ 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.

Détail

DOI : 10.2140/gt.2015.19.237

Classification : 32V05, 57M50, 22E40
Keywords: spherical CR structures, geometric structures on $3$–manifolds, complex hyperbolic geometry

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